Goddric is a 1/1 Citizen. With Dress Down, Goddric is instead a 4/4 Dragon.
The abilities
Goddric's ability says
As long as two or more nonland permanents entered the battlefield under your control this turn, Goddric, Cloaked Reveler is a Dragon with base power and toughness 4/4, flying, and "{R}: Dragons you control get +1/+0 until end of turn."
Witness Protection's ability says
Enchanted creature loses all abilities and is a green and white Citizen creature with base power and toughness 1/1 named Legitimate Businessperson.
And, Dress Down's ability just says
Creatures lose all abilities.
The rules
These are all static abilities that create continuous effects, so they are governed by the Interaction of Continuous Effects rules, also known as the layers rules. For reference, the layers are listed in rule 613.1:
613.1. The values of an object’s characteristics are determined by starting with the actual object. For a card, that means the values of the characteristics printed on that card. For a token or a copy of a spell or card, that means the values of the characteristics defined by the effect that created it. Then all applicable continuous effects are applied in a series of layers in the following order:
- 613.1a Layer 1: Rules and effects that modify copiable values are applied.
- 613.1b Layer 2: Control-changing effects are applied.
- 613.1c Layer 3: Text-changing effects are applied. See rule 612, “Text-Changing Effects.”
- 613.1d Layer 4: Type-changing effects are applied. These include effects that change an object’s card type, subtype, and/or supertype.
- 613.1e Layer 5: Color-changing effects are applied.
- 613.1f Layer 6: Ability-adding effects, keyword counters, ability-removing effects, and effects that say an object can’t have an ability are applied.
- 613.1g Layer 7: Power- and/or toughness-changing effects are applied.
Goddric's effect works on layers 4, 6, and 7. Witness Protection's effect works on layers 3, 4, 5, 6, and 7. Dress Down's effect only works on layer 6. Layer 7 is actually divided into sublayers, but both Goddric's and Witness Protection's effects apply in the same layer:
613.4b Layer 7b: Effects that set power and/or toughness to a specific number or value are applied. Effects that refer to the base power and/or toughness of a creature apply in this layer.
There is one other rule that is important to consider here, with effects that apply in multiple layers and effects that remove abilities:
613.6. If an effect should be applied in different layers and/or sublayers, the parts of the effect each apply in their appropriate ones. If an effect starts to apply in one layer and/or sublayer, it will continue to be applied to the same set of objects in each other applicable layer and/or sublayer, even if the ability generating the effect is removed during this process.
This is the rule that the ruling on Goddric quoted in the question is based on. Now, the final piece of this puzzle is seeing how multiple of these effects are applied to the same object, and this is determined by the timestamp rules:
613.7. Within a layer or sublayer, determining which order effects are applied in is usually done using a timestamp system. An effect with an earlier timestamp is applied before an effect with a later timestamp.
- 613.7a A continuous effect generated by a static ability has the same timestamp as the object the static ability is on, or the timestamp of the effect that created the ability, whichever is later. If the effect that created the ability has the later timestamp and the object the ability is on receives a new timestamp, each continuous effect generated by static abilities of that object receives a new timestamp as well, but the relative order of those timestamps remains the same.
- [...]
- 613.7d An object receives a timestamp at the time it enters a zone.
- 613.7e An Aura, Equipment, or Fortification receives a new timestamp each time it becomes attached to an object or player.
The results
Goddric + Witness Protection
So, in the situation with Witness Protection, Goddric must have entered the battlefield before the Witness Protection became attached to it, so Goddric has the earlier timestamp, which means that Goddric's effect has the earlier timestamp. As a result, the effects are applied like this:
- Layer 3: Witness Protection makes Goddric's name "Legitimate Businessperson".
- Layer 4: Goddric's effect makes Goddric a Dragon, then Witness Protection overwrites that, making Goddric a Citizen.
- Layer 5: Witness Protection makes Goddric green and white.
- Layer 6: Goddric's effect gives Goddric flying and "{R}: Dragons you control get +1/+0 until end of turn," and then Witness Protection removes all of Goddric's abilities.
- Layer 7b: As a result of rule 613.6, even though Goddric lost its ability in a higher layer, the effect continues to be applied in this layer. Goddric's effect makes Goddric a 4/4, and then Witness Protection overrides that, making Goddric a 1/1.
As a result, Goddric is a 1/1 green and white Citizen with no abilities. The reason that the result looks the same as if we only applied Witness Protection's effect is that it just happens that Witness Protection has an overriding effect on every layer that Goddric's effect works in. If we replaced Witness Protection with Kasmina's Transmutation, for example, Goddric would end up as a Dragon.
Goddric + Dress Down
With Dress Down, we instead only apply Goddric's effects except in layer 6, like this:
- Layer 4: Goddric's effect makes Goddric a Dragon.
- Layer 6: Goddric's effect gives Goddric flying and "{R}: Dragons you control get +1/+0 until end of turn," and then Dress Down removes all of Goddric's abilities.
- Layer 7b: As a result of rule 613.6, even though Goddric lost its ability in a higher layer, the effect continues to be applied in this layer. Goddric's effect makes Goddric a 4/4.
So, the result is that Goddric is a 4/4 red Dragon with no abilities.
Goddric + Dress Down (Dress Down enters first)
One other possibility here is that Dress Down entered the battlefield before Goddric, giving it an earlier timestamp. In that case, the only difference is that layer 6 goes like this:
Dress Down removes all of Goddric's abilities and then Goddric's effect gives Goddric flying and "{R}: Dragons you control get +1/+0 until end of turn."
The result here is that Goddric is a 4/4 red Dragon with flying and "{R}: Dragons you control get +1/+0 until end of turn."
Bonus: Goddric + Kasmina's Transmutation
As mentioned in the section about Witness Protection, you would see a different outcome with Kasmina's Transmutation. Here's the details of how those effects would be applied:
- Layer 4: Goddric's effect makes Goddric a Dragon.
- Layer 6: Goddric's effect gives Goddric flying and "{R}: Dragons you control get +1/+0 until end of turn," and then Kasmina's Transmutation removes all of Goddric's abilities.
- Layer 7b: As a result of rule 613.6, even though Goddric lost its ability in a higher layer, the effect continues to be applied in this layer. Goddric's effect makes Goddric a 4/4, and then Kasmina's Transmutation overrides that, making Goddric a 1/1.
The result is that Goddric is a 1/1 Dragon with no abilities.