I'm not sure it's grammatically wrong. An English speaker would more likely say "You probably don't play", but "probably" and "likely" are both adverbs in this sense, so either should work. Likely is more often used as an adjective, but is occasionally used as an adverb. Probably is an adverb. Update: Some sticklers claim that likely is only an adjective, especially British English sticklers. As a matter of actual usage, it's rather common in American English.
Your examples don't state why it's grammatically wrong; on the contrary, using "wouldn't" changes the meaning from present to future. As it turns out, it's not grammatically wrong. "You do likely not play" or "You don't play likely" are grammatically wrong, but the placement of "likely" is otherwise quite flexible.
For an example where this sentence is fine, albeit probably not the most common way to say this in spoken English: If I'm talking about how boring baseball is, you may wish to contradict me and point out that it's very exciting for the players, who must constantly remain on guard for the ball to come their way. "You say baseball boring, but I understand why you might say that. You likely don't play."
That is very awkward as an English sentence. Another correct way to say this would be "They probably aren't playing". The "likely" (wahrsheinlich) also pertains to "probably". It is "likely" and it is "probable" are interchangeable, but should be used with caution in English to avoid awkward sentences.
Can anyone post me link to an article explaing the order of of scentences in German (or tell me), obviously this one directly translate to "They/You play probably not" Why is that? I would really like to understand what makes the scentence structure/ grammatical order in German, so I can formulate my own scentences!