Absolutely. I think the natural English (I'm Canadian) phrase would be, "I don't even have to try"
For what it's worth, I (native US English speaker).don't see anything at all wrong with it, and I can easily imagine saying or hearing someone else say it. Might be used to give a little more emphasis than "I don't even have to try"... Something like "I don't even have to be TRYING to win when I play chess with him... he's soooo bad..."
I can see your point, but without those extra qualifiers this definitely seems like czenglish to me as well
Sorry, but I (also a native US English speaker) find this sentence very unnatural. "Have" is acting as the main verb, so it would be followed by an infinitive, no? EX: "I have to sell more cookies." When it's followed by a continuous form (not to mention negation) it sounds strange. In your example, we would say, " I don't even have to try to win when I play chess with him... " This is a statement about a general truth and would require the present simple, not continuous.