In general, I would consider a game be "beaten", when I see the end credits roll.
Though, I do remember (action-y) games of my youth, that had no end credits to reach.
After "beating" those games' "last" level, the game simply jumped back to the first level - which you then tried to play through, but now against more enemies and/or with heightened game speed.
In particular regard to your examples, I would also differentiate between "(merely) beating" a game (= seeing its end credits roll (if available)) and "completing" a game (= collecting/unlocking 100% of the content a game may offer).
Because the first can and (arguably (?)) should be possible, without collecting/unlocking everything a game has to offer.
I'd say, that first option is meant for "gamers (in general)", while the second option is (only) for the "completionists" among the gamers.
(And often enough, the second option is first and foremeost meant to feign a longer playtime than there actually is).
In that regard, I also think, it's important to note that - to accomplish a 100% completion - it is probably necessary to (completely/in parts) play through a game several times.
Which is an option, that is simply not interesting for many (most?) gamers, which usually have a (more or less huge) backlog to yet play through - for the first time.
And last but not least: from time to time, and with some games, we simply have to accept, that a game will beat us - instead of the other way 'round.
Edit:
I just remembered a game where I didn't even bother to complete all unlocked side quests anymore, after 20 to 25 hours in the game: "Two Worlds".
I consider that game "beaten", because I beat the end boss and saw the end credits roll - despite still having a list of undone side quests.
But after 20 to 25 tiring hours of
"getting a side quest in village A,
move to village B, get a hint, that the side Quest from vilage A can be finished by visiting village C,
moving to village C, receiving an important item mentioned in side quest,
moving back to village A, only to get send to village B again to get something else necessary for completing the side quest - from the very same NPC with which you talked earlier"
...rinse and repeat that for basically every side quest...
I was fed up with the game and its side quests.
Post edited January 04, 2024 by BreOl72