In practice do competitively viable decks have approximately similar ratios of card types? There are CCGs in which this is empirically observed, such as Pokémon (2-3 trainers: 1 Pokémon: 1 energy) and Yu-Gi-Oh (2 monsters: 1 spell: 1 trap).
Note: "type" in this context is not intended as the MTG technical term, unless that interpretation would give an affirmative answer. Essentially the question is whether any pie-chart generalisation for structure is applicable in practice.
Deck construction varies greatly from format to format, and even counting in formats that are more commonly played competitively with constructed decks (Modern, Standard, maybe Legacy) or limited formats (Sealed, Draft), you will find a great difference in deck lists.
Limited formats have the unique feature that you have to work with which cards you open or pick, meaning that while you might get lucky and draw some mana fixing, it will very likely not be enough to alter your mana base significantly because of it.
This will also largely depend on the edition you're playing with - while for most editions you're not too bad off playing 17 or 18 lands, Kaladesh is an edition where you will be suggested playing only 16 lands, due to the overall lower mana curve and speed of the format, and as far as I've noticed it, this is what highly competitive players actually opted for.
Due to the relatively low chance of building combo decks (due to not all editions featuring combo-enabling cards, as well as you not always drawing them), most Limited decks will have a great number of creatures compared to other nonland cards, as those are able to threaten damage over multiple turns, as compared to an Instant or Sorcery.
Constructed is any entirely different animal. Not only do you get many different decks due to the different win conditions - you also can substitute card types you would normally use with others.
The consensus of comments and the first answer seems to be that lands, other than other card types, do have a recognizeable, repeating amount among decks. I would dispute that, due to the fact that MtG provides many different ways to come by the same resource.
To name an example, while you would normally produce red mana with a Mountain or other land card, you might opt for a Simian Spirit Guide (Creature) or Lotus Petal (Artifact), while other decks may still play the basic land, even for one and the same deck concept.
Another factor is how much mana your cards actually require to cast, and how long you intend to play before you win. Modern Affinity is notorious for dropping large portions of the starting hand into play on the first turn for having many cards that cost no mana to cast, resulting in a land base of 16 or even less lands (such as 12 back in 2011). Whichever conclusions you draw from that, and whichever average number you include it in, you will end up with a number that has nothing to do with reality, as the right number is not the average between 24 and 16 - it's 24 for one deck, and 16 for another.
As for other types, you're just completely entering random number territories. Decks will play their combo pieces, which can be any random card type - they are included because they're a part of a combo and do their job, not because the deck needs an arbitrary amount of a certain card type.
To again name an example, if you look at Splinter Twin deck lists, you will commonly find 4 copies of Splinter Twin, which is an Enchantment/Aura card. It's the key card for this very deck, but even considering adding a set number of Auras to a deck because it works for a single deck is ridiculous, as they make you weak to get "2-for-1-ed", meaning that you lose two cards to a single removal spell, for example. Not just including this card in a deck, but deciding to build entirely around it is what makes the deck strong and playable, but all of this is entirely independent of the card type - what matters is the card function.
I don't think you can create an accurate and purposeful diagram over the entire span of MtG competitive formats or decks. What you can attempt to create such a statistic for an individual format, but that will likely give you an average number with no practical purpose, since after all, you're likely not looking for a diagram with decorative qualities, but one to look at it and say "I should probably play n of that type to be successful", and I do believe such a diagram cannot exist for the entirety of the MtG universe.
Since you mentioned other TCGs in your question, let me also mention that MtG has a lot more formats that any other card game I'm aware of, making the issue of a general analysis even more of a complex dilemma, and the lack of this diversity in other formats may well be the reason that such a simple breakdown is possible for those games, but not MtG.
In this answer, the mentioned formats from my introductionary paragraph are the only ones I even considered - there are other formats played competitively, but not to an extend that makes their mention particularily worthwhile or representitive. Whichever numbers you might come up, once you enter Vintage Two-Headed Giant Commander (a format entirely covered by the official rules, mind you, yet not particularily tournament-viable), you will realize they won't work out even by a long shot.
There generally is a standard ratio when it comes to the Land type, but not with other types. Most newer players will start out with a recommended 24 out of 60 cards being Lands (40%).
However, this ratio is far from fixed. As you get better with deck building, you learn that different decks have different needs, and it's common for decks to have less, or sometimes more, than 24 lands. Some decks even have no land at all!
Also, competitive decks are even less likely to follow this than beginner/casual play. This is because there are so many different types of competitively viable decks, as well as the fact that there are many different formats for competitive play, with different cards and sets being legal. So there is no one right type of deck, or even one right type of format, for competitive play.
There are several other types of cards, and those types don't have any sort of standard of how many there should be. Some decks might be creature heavy, others might have little to no creatures, for example.
There are several other questions dealing with the specifics of how many lands to have, here's a few examples:
How many lands should I have in my sealed or draft decks?
How should I determine how many lands of each different color to put in my deck?
(Thanks Rainbolt for finding those links).
In limited formats, you tend to want about 17 lands, 14-15 creatures, and 8-9 other cards.
In constructed formats, because you have a wider selection of cards and minimal limitations, you are not as limited by what kind of win conditions you can use. You don't necessarily need to depend on creatures to reliably kill the opponent. You can make a wider range of strategies work. There are decks like Lands that play nearly all lands. Most of the spells in Enchantress are enchantments. There are burn decks, control decks, and storm combo decks that all play nearly only instants and sorceries. There are manaless dredge decks that play no lands.
The only common pattern that you need to know about in constructed is that your mana curve should be a reflection of the amount of mana sources you play. If your strategy necessitates large mana requirements (e.g. if the average mana cost of the non-land cards you want to play is 2.9), then you need to play more mana sources (e.g. 26 lands instead of 24/25 lands), and then your mana curve should be adjusted to be an ideal fit for a 26-land deck (e.g. 4x 1-mana cards, 11x 2-mana cards, 7x 3-mana cards, 5.5x 4-mana cards, 3x 5-mana cards, 1.5x 6+-mana cards, 1.7x X-cost cards, some mana dumps).
