Marauding Raptor has a damaging component, and an effect based on if damage done & creature type match, but it's not worded as straight forward as traditional Enrage cards.
Marauding Raptor isn't an Enrage card and isn't meant to be seen as similar to one. Instead, it was designed (in the same set) to enable cards with the Enrage mechanic. It deals damage to another creature; the idea is that you play this in a dinosaur tribal deck where "another creature" has an enrage ability, so you get synergy (at the expense of marking damage on the creature, which could kill it or make it temporarily more vulnerable).
The effect reads:
Whenever another creature enters the battlefield under your control, Marauding Raptor deals 2 damage to it. If a Dinosaur is dealt damage this way, Marauding Raptor gets +2/+0 until end of turn.
This is one effect, that is resolved all at once. The +2/+0 result is conditional, but it is not "triggered" by the damage that Marauding Raptor did to the other creature. Therefore, Wayta does not interact with this.
A triggered ability starts with "when" or "whenever", not "if". The entire effect is triggered by a creature entering the battlefield under your control - and not by a Dinosaur being dealt damage "this way". The phrase "this way", incidentally, is another hint that this sentence does not define a separate effect.
Does Wayta care about "Excess Damage", and when those effects trigger?
Wayta does not make any particular distinction regarding excess damage. However, to deal excess damage entails dealing damage. Maarika says
Whenever Maarika deals damage to a creature, if that creature was dealt excess damage this turn, that creature’s controller sacrifices a noncreature, nonland permanent.
That's a triggered ability (it starts with "whenever"), with an "intervening if". If Maarika deals damage to "a creature you control" while you also control Wayta, then "a creature you control" is "being dealt damage", and that event "causes a triggered ability of a permanent you control" to trigger (since we're in a situation where "Maarika deals damage to a creature"). When a source deals damage to a permanent, damage is (ordinarily) dealt to that permanent. The dealing and the being-dealt are not treated as separate events, since nothing can happen in between.
Therefore, Wayta's replacement effect ("If...") takes effect, creating another instance of the triggered ability. Each instance will then check whether "that creature was dealt excess damage this turn" (and normally the answer will be the same each time that's checked); for each instance where the condition was met, "that creature's controller" (which will normally be you, each time) sacrifices a noncreature, nonland permanent.
However, all of this depends on Maarika dealing damage (it doesn't have to be combat damage) to your own creature, while you also control Wayta. If for example you control Maarika and you attack an opponent who controls Wayta, and your opponent chump-blocks Maarika, Maarika's effect is not doubled up. That's because the triggered ability (on Maarika) that was "caused to trigger" by the excess combat damage, was not a triggered ability "of a permanent you control" (from your opponent's perspective).