I'm preparing the website of a game I develop (and will be released next year).

In its description on the website, I want to mention that it's similar to another game (which was very popular btw). I'm not affiliated with that game. For example, the text can be:

The adventures in this game are similar to the challenges in <thirdpartygame>

I checked and the name of the 3rd party game is a trademark. Do I have to write <thirdpartygame>TM along with a trademark text in the page footer, or it's not needed? I read about "nominative" use in wikipedia but that's probably not relevant here.

(I will probably also mention that I'm not affiliated with that game, and was only a fan of it.)

You mentioned nominative use, and actually, yes, that is exactly what applies here. You are using the name of a product to reference the other product.

Be very careful about how you use it. Generally no, you don't want to put a TM or other mark over it. You don't want to call out any special attention to it. You are simply using the name. Try to avoid it since it can cause problems, but ultimately the names of other brands are still words, they are not banned from your lexicon if you need them.

Don't do anything that could even remotely be considered an endorsement or a relationship between you and them. Don't use their logos or other marks, their taglines, their brand phrases. Just a simple name, the minimum amount you need to make a reference, which is called nominative use. I would be cautious about your usage and see if there are ways to describe the genre without using the other game's name. But ultimately if you do want to make a list of games it is similar to, you would be hard pressed to do it without using their names. Your lawyer (if you have one) may recommend a blanket statement like "names of products are trademarks of their respective owners" to make it more clear you aren't trying to say Activision/Blizzard or Valve are endorsing your game or that you are using their trademarks to mingle with your game.

Thanks. I won't have a list of similar games, and the whole website will only mention this 3rd party game once. And the rest of the text won't imply that I'm endorsed or affiliated in any way with the 3rd party game. Moreover, my game isn't even generally similar to it. So it will look like this (not with Warcraft 3, but I want the example to sound "realistic"):

The adventures in this game are similar to the challenges in Warcraft 3.

Question: what is the worst case? OK, I know anything can happen, but a "realistic" or "typical" worst-case? How would the legal owner/holder of the name act first time? Because if they just send me a cease-and-desist, I can remove the reference and that's it. But if they sue me for a lot of money (as a damage they suffered for some reason), that's not OK.

Usually, in cases such as this, is there any "actual" negative consequence one would need to face, or usually a removal would solve it?

I don't know about your particular situation but I do know that for submitting an app to apples app store if you mention a third party app in your discription it can result in your game being rejected

So whilst this may be slightly different than your scenario, I think if Apple are cautious about this kind of thing then maybe you should be too.

I see. I am talking only about a website, and game will be for Steam store, not Android/iOS, but thanks.

Question: what is the worst case? OK, I know anything can happen, but a "realistic" or "typical" worst-case? How would the legal owner/holder of the name act first time? Because if they just send me a cease-and-desist, I can remove the reference and that's it. But if they sue me for a lot of money (as a damage they suffered for some reason), that's not OK.

Usually, in cases such as this, is there any "actual" negative consequence one would need to face, or usually a removal would solve it?

Worst case could be extreme. Lawsuit over trademark infringement, trademark dilution, unlawful competition, misappropriation, and more.

More realistically if they were upset it would be a C&D order demanding your web site remove all references to their products, services, names, and trademarks.

Generally it is bad form for you to do it unless there is no other way for you to do it. But sometimes there is no other way to express it. As I wrote above, if possible describe the genre and the activity rather than naming the product.

As an example, if you were building a review website comparing multiple games, it would be impossible to review the games without giving their names. You don't need to include their trademarks or other things, but in those cases you would need to give specific names to things.

I personally would not want to include it. You are saying "this game is a knock-off of a cool game", which tells people they should go get the other game instead.