Do people actually think about theories while playing?


I don’t think about theory as, “my opponent slipped up, here is the proper punishment” per se. I think of, “this is a move I don’t usually see. How suspicious is it?”
Also, it gets easier to memorize lines once you understand the ideas behind the lines. So it’s not so much memorizing specific moves for me, as it is memorizing the ideas that I should look for in specific positions.
Frankly speaking, the better you are at the game, the more you will be able to memorize since the moves will make sense as they contribute to some objective (it's like literally any subject in the world).

Do not worry about memorizing anything - whether it's moves or names of openings. When it comes to openings, instead of memorizing you should learn and understand the Opening Principles https://www.chess.com/lessons/opening-principles
Eventually you'll start memorizing the moves almost by osmosis because they'll came naturally and you'll understand what the moves are trying to accomplish.
With time, just from seeing the names of the openings you'll recognize "oh this is the italian game, this is the sicilian defense, etc etc"
But do not worry about "opening theory" and memorizing the moves because even if you do memorize the moves, chances are your opponent won't know the theory and will play something different and you won't know what to do, which is why is important to learn and understand the previously mentioned opening principles
Good Luck

I play a hypermodern game and rely on ideas not theory nor opening principles:
https://www.chess.com/game/live/44598551583
https://www.chess.com/game/live/40451975359
https://www.chess.com/game/live/24620535969
I can assure you I read no books and just winged it! Have fun and free roll it.
I just couldn’t grasp the 1.e4 and 1.d4 stuff from (both sides ) so I bypassed the heavy theory and popular opinions.
Working out well ever since!