Yes and no.
Yes, it has a prefix to show the subject and the object -- but the prefix for "subject = third person singular (he/she/it); object = third person singular (him/her/it)" is the null prefix or empty prefix: nothing at all.
So Suv has an empty prefix, which looks the same as no prefix (as if you had forgotten to add a prefix).
Suv can thus mean not only "he fights" but also "he fights him" or even "he fights them" and "they fight" and "they fight them". (But not "they fight him" -- that combination of subject and object does have a prefix.)