one very niche example i'm personally invested in is 200% Mixed Juice, a short pseudo creature collecting retro jrpg that happens to have online pvp. i really like it, though i've also been involved with doing a balance overhaul patch for online use which i consider "essential" for it specifically, rebalancing close to everything and making a few more units playable, rectifying some overpowered unit issues that were never patched out officially
i would definitely still say i consider the game really good without it though, especially since it was only done to iron out balancing quirks for one side of the game, obviously it's not an issue for the singleplayer (save for missing out on some minor/boss units being playable). it's an odd matter though since while the singleplayer IS the main draw for the game, the main reason the multiplayer isn't a bigger one is just because the game has no playerbase...
still yeah i don't think a must-have mod
necessarily
covers the full scope of "this game cannot be played without it", it can depend on what it's for. if you are playing something where the core gameplay experience is a hot mess without them then yeah that'd be something i'd very much be reluctant to praise