Grammatically, this sentence is correct.
However conceptually, the word 'go' is not so meaningful since this sentence has not specified the place of playing football. For instance, 'I go to the playground to play football.'
You must write,and not write:-
Prime tense=Present tense=present (adj) time with verb eg:-be,have,
eg:-I go to play; I go to work; I like to play; I get up at; I start for football ground; I am called Tom.