I’m one of those people you’re probably referring to. I love writing about games after I finish them so I’ll give you my process. And you can see my approach in action on my posts.
Basically what I do as I play is I do miniature reviews at certain points. These mental pauses act like checkpoints for me and usually happen after each play session. I think about what I enjoyed and what I didn’t and what interesting mechanics there are. I really tear the opening of a game to bits and then reassemble it so that I know what it is I’m playing.
Now I myself don’t typically need to take notes, but I feel like I could and it would help me remember certain details. If you find yourself forgetting early parts of the game, do take notes.
I personally talk about games here because I like the innovation and the actual art that games are apart of. Think about the soul of a game and what that looks like. Think about what the soul of a game like Stardew Valley looks like. Its soul is about connection to characters, self improvement, community. It’s the human emotion or ideal aspects to a game. Then take those soul components and see how they’re attached to levers in the game. Ask yourself how the game gets you to feel the soul ideas as tangible. Then talk about all of that in sectioned out pieces starting with most important ideas.
Hope this helps! Feel free to ask more or send me stuff if you want me to review anything :)