The whole usage of memes in games is something that can be good or bad, like most things, it just depends on how it's used.
Using mentioned examples:
"One does not simply" is a pretty subtle meme that most people probably wouldn't even see as a meme if they didn't know any better. It's a fairly standard sounding line for say, a medieval setting, but might sound out of place in a futuristic setting, especially from a character that isn't really refined. So it can come off as a natural line in a lot of games (while still being a LoTR shout out), but might sound out of place in others.
On the other hand, the "doge" meme is just going to stick out as an obvious, forced meme no matter where it's used, and is only really fitting in games that do not give even a remote care about the fourth wall from the get go, like say, the Deadpool game.
Then there are memes that are sort of relevant to the subject matter. Smash 4 for example, references "my body is ready", which is appropriate since it's a popular Nintendo meme in a Nintendo celebration game (that also doesn't give a crap about immersion or the fourth wall to begin with). And a lot of the reason the Sonic social media is so popular is because it references actual Sonic memes most of the time ("Sanic", "Gotta go fast", "& Knuckles", Big the Cat in general, etc).