Were any of those games not known as exclusives at the time of review? If so they should probably be excluded.
I'm also not sure why the list would be missing some 3DS games because of reason #2. 3DS games are Nintendo games in the same way that Fire Emblem Warriors is a Nintendo game for example. What games do you consider Nintendo games as opposed to Nintendo exclusives, and how does it relate to the 3DS games you're referring to that are missing?

The only joke I made was the "Bias against Xbox exclusives" portion.
The difference is that I implied it immediately. It wasn't an afterthought that I edited in afterwards. Not sure how you thought I would take your comment as a joke without the second line you edited in afterwards, which indeed I did not see, but if you say it was intended as a joke I'll give you the benefit of the doubt.

Here's the thing. Me disagreeing with your method of gauging bias does not mean that I'm automatically saying that they are biased.
I some times disagree with methods regarding opinions I agree with, and they often presume I disagree with the opinion as well.
Although in this case I don't agree with any conclusion. But I would entertain the idea by looking at proposed evidence. And I think the way Barkley tallied scores is a more relevant way to gauge this because there are more ways to give preferential treatment than just the highest possible score.

I think it's fair to say that Edge in recent times generally give lower scores across the board than most publications. (That may very well be because they make use of the full scale of the scoring system better.) And also that in the past year or so they've given Playstation exclusives notably lower scores than for Nintendo. That may just be a coincidence. If anyone wants to extend that list back a few more years, I'd be interested in seeing if it changes.

Either way, scores by themselves don't say much to me. I'd have to read the review to know if the game is to my liking and if the reviewer considered the things I like a positive or negative.
For example:

Persona 5 :                          Meta - 93         Edge - 80
Nier Automata :                 Meta - 88         Edge - 80
Arms                                  Meta: 77    Edge: 90

ANyway, Edge just wants to be different unless it's key Nintendo franchises. They are definitely checking out meta before they place their own scores while everyone else just scores how they feel about the game. And when it comes to Nintendo, everyone just treats them like they no their stuff simply because they were the first in the business. I know for a fact that is the reason. They DO make great games, but honestly they are no different to some of the great games other companies make now.

GoW was only 1 point behind Arms!, couldn't quite get that 9/10. A real shame!

I see, so you think he picked games that were published by Nintendo and/or featured a Nintendo IP?
I'll let him answer whether or not that was his intention, but right now I agree with you that the games you mentioned should count.

Because of the many factors that are unknown to me at the time, and in absence of a larger sample list of reviews in recent years, I wouldn't conclude that those are the only two scenarios.
But I'll say this. If people on the internet can have a certain mindset, then someone working at Edge or any other publication can as well.
Edge is more heavily weighed on Metacritic, and they are at least aware of that, and the fact that their reviews can get extra attention because of this. But if they presumably take advantage of this, it could be for sensationalism rather than platform bias.

The list Barkley provided was interesting though, but it was a pretty small sample size, so I wouldn't draw any conclusions based on it. A larger list would more interesting.
But personally, if we're going to compare lists I'd be more interested to see how so called 'critically acclaimed' games measure up to each other. Which is hard to define, but perhaps games that score 85 or above. The reason those titles would be more interesting to me is because they tend to generate more buzz and attention. And if we're talking exclusives, an ability to drive console sales.