More than 10 years ago I played a little game that was developed (I think) over a week-end. A side-scrolling game, 4 block high, one spritey character that can only go forward and walk around obstacles (block of colours). The character gets older and older and always dies in the end. There are weird items you can pick up and seems to increase your lifespan but that's it. At some point you can meet another character and if you choose to walk with her then there are less path you can take. But if your character dies then you switch to that other character. The author said it was to show there are things you can't do or have to differently when you become a couple. The game was 2 minutes long, top and it was some kind of comment on life, nothing more, nothing less but I still think it had a deeper connection to the player than Gris, Celeste or Oldman's Journey could ever have (well at least it did with me). I think those games just scream to the player what to feel and when and I think it's less interesting. End of rambling ^^. I am trying to find the game back by looking at IGF festival archives but no lock so far.
Similarly, there was a game called Brothers that delivered its punchline through its mechanics in a powerful way. (I don't want to spoil it for anyone!) I'm not sure if it's art or whatever, but it's something interesting and distinct from what you get in other forms of media.
Meanwhile, I enjoyed both Gris and Celeste, but purely on a mechanical and/or aesthetic level, and not really a connection to any deeper message.
I think what you bring into the piece of art you are looking at/into (or rather immersing yourself into) matters as much as what the author put into it. So I do agree with you, "where it's coming from" is always interesting to follow. Sometimes it doesn't click on the level we want to click but that's okay, maybe it'll click later (sometimes you need to experience some things IRL to really understand what was going on with a piece of art that didn't click and sometimes what you experienced in real life will make it unbearable to look at some art evoking it).
Regarding Gris: yeah, the hype didn't help. But I poured 3-4 hours into the game on 2 different occasions and the game did bore me and I didn't find what I was looking at interesting, at least not enough to keep me playing.