When is a game idea stealing?

Do i risk getting into legal issues if my game looks a lot like World Of Warplanes, even though i did not steal anything from them?

Yes. You risk getting into legal issues by just breathing!
But if they sue you for making a game about warplanes, then when you go to court, you can ask them to prove that you stole something.
An overall idea ("game about warplanes" or "game about building warplanes" or "game about WWII warplanes" or "game about warplanes in August 1943 in Italy") is not protectable. In other words, it's common that people develop similar ideas. There must be a lot of differences between your game and theirs.

Like Tom said, they would have to prove that you stole something. However, is there any possibility that you may have unconscionably knew about this idea before you started working on it? The courts will look at how likely it is that you have seen something with their game before you started working on yours. If they feel that it is likely that you were aware of the World of Warplanes before you started working on your game, they make call it copyright unconsciously (which is just as illegal as if you purposely stole it). I'm not saying this is the case for you, but it may be. I know someone who went through the same situation. If World of Warplanes had no national ad or way to reach you then you should be fine.

A side note: If somehow you and them produced the exact same game without either of you knowing that the other game was in production, then there would be no copyright if you cold prove it. This has happened a handful of times in copyright law for music (and it was quite fascinating, personally). So just some food for thought.

P.S. Standard Disclaimer: do not take this as any sort of official legal advice

A side note: If somehow you and them produced the exact same game without either of you knowing that the other game was in production, then there would be no copyright if you cold prove it. This has happened a handful of times in copyright law for music (and it was quite fascinating, personally). So just some food for thought.

http://en.wikipedia.org/wiki/Multiple_discovery