You've got a lot of replies already advising you to play this game because you've already paid for it. I'll add on to it.

I completely understand how you feel about contributing to their power. I have my own struggle with blizz because while I despise them, they make the only game that all of my friends want to get together to play. It's infuriating.

You are correct that they get something out of you playing the game after you've paid for it. A video game company basically trades on sales, market presence, and monthly active users (MAU). The first two are essential to their success, but MAU is a bit trickier for them to extract value from. The strategy is that MAU is a metric by which they can curry favour with investors, or it gives them an idea how much they could earn from continuing to support the game or creating a sequel, or the potential value of crossover events.

However, MAU also comes with direct costs to the company. As you say, the game runs on their servers even when played against no human players. You cost blizz money every time you play it. That cost, honestly, is pretty negligible. But, the benefit that they get from one single active user is also negligible.

Something I think about is how difficult it can be to protest a game. The saying goes is that even bad publicity is still publicity, and this is true of games. For instance, when people talk about boycotting a game, the name of the game ends up in the news where it will have a wider reach - potentially to people who don't care about a boycott and are hearing about a game that everyone's talking about.

This is something that comes up in the piracy community too. A common defense of piracy is that it's actually good for the company: people who weren't going to pay for your game are still playing your game and talking about it. They inspire their friends and strangers to play this game, and if they really like it then they become potential customers when they can afford to do so.

My belief is that the two best ways to support a game are through purchase and word-of-mouth. You already paid for the game, so there's nothing you can do about that. However, if you don't want to feed the beast, the best way to deprive them would be to simply not talk about the game. Don't name it, even to shame it

This is a rare case where keeping quiet can ease your conscience.

Is the game you're thinking about a famous real-time strategy game? They have a few that I'm nostalgic for but I've never been able to get running on my computer in recent years. Modern RTS games tend to be a bit different, and they just don't scratch the same itch. Happy to be proven wrong if someone knows some indie darling though.