It's only "I go to play tennis." "Tennis" is the activity, and play is simply the verb. If the activity is a gerund (jogging, swimming, etc), then you can use it directly: "I go swimming." "I go for..." is only used when the activity is a simple noun and not a gerund. "I go for a game of tennis." "I go for a walk." "I go for a drink."

An English speaker would understand that you play tennis but they would be confused. I am going to play tennis this afternoon. You will play tennis. I am leaving now to play tennis. You are going to play very soon. Note that you can write "I go to school" meaning that you do go to school. You may also write that you are "going for two hours". In this case, the "for" has to do with the time you plan to spend playing tennis. I am going to play tennis. This says that you intend to play tennis at some time.

it's simple to say " i go to play tennis" or " i go for play tennis"

http://www.eslcafe.com/grammar/verb_forms_and_tenses05.html Questo link può essere utile.

I think it is better to say "I'm going to play tennis."