To be more specific, gamers get annoyed when they have to install yet another "game manager" program to play a game. This is especially true when that game manager is well know to lack features and be insecure.
Installing a game standalone doesn't annoy anyone I know (though, to be fair, I'm now older with few friends)
And to generalize it a bit - users get annoyed when they want to just buy a product, and the producer pulls some vendor lock-in bullshit trick. They're right to be annoyed, because not only it is inconvenient, such moves are meant to exploit them.
"Game manager" is a especially visible case because, with the exception of Steam, Battle.Net, they're almost universally crap. Some of them are so bad I wouldn't want to install one even if it was the only game platform in existence!
You normally have to create an account to get the new game manager to work as well. Now I'm trusting yet another company with my account details, and had to "accept" a bunch of terms and conditions all totally unrelated to the game I want to play.
FFXIV from Steam requires the download and usage of the abysmal launcher it has. As an added bonus, when you buy the game on Steam, you're locked in to Steam releases going forward: can't buy Shadowbringers from FFXIV's site, you must buy it from Steam.
Every Ubisoft game since Black Flag that I've bought from Steam has required Uplay.
I'm sure there are other examples, but Steam isn't preventing users from being hit with another "game manager" download. In some cases, it facilitates it.
Installing a game standalone doesn't annoy anyone I know (though, to be fair, I'm now older with few friends)