I feel like I'm reasonably good at picking at a game on the gameplay level, as per what works and does not and why and surface videogame essayist stuff like ludonarrative dissonance (or the rare examples of ludonarrative harmony).
I may offer you my finest insight into video games such as "Lara Croft has some sort of father complex going on" and "Shadow of Chernobyl is unintentionally about life in the collapse of the soviet union" which even by my own admission feels shallow and trite. You watch someone like Jacob Geller or Noah Caldwell-Gervais and they have fascinating things to say even on games you wouldn't expect it, like NCG on Quake.
How do I become that knowledgeable? Interesting? Analytical? about video games?
The joke in the meme is that the ogre does understand it he just can't admit to himself that that he understands it. Actually getting the references through study doesnt carry with it a sense of accomplishment, we dont focus on the accomplishment of knowing more than we once did, we focus on the recognition of all that we dont know.
As for games, I really only got really into lore with Bloodborne. it took a huge amount of playing, watching videos, talking to people in group chats, looking up references, hunting down clues. I imagine if youre really into that kind of work, it starts to come easier the more you do it. But those creators are intentionally engaging with the game in a way beyond just the gameplay. If you play games to play games, then yeah you might miss that stuff. But if you play games and then do a bunch of meta study and research on them, then you'll get more of that out of them.
Just find discord servers for games you like and talk to people about the story, stuff youre curious about, etc.