Translation:I do not think that he plays with that team.
It is, but with a few exceptions (mostly idioms) we rarely use the English subjunctive nowadays, and certainly not in speech. The Italian coniunctivo has specific usages (uncertainty, change of subject in sentence ...) and to translate it into the English subjunctive is a potentially embarrassing mistake.
La squadra can mean a squad, or indeed a squadron. However, you may have noticed lui giochi = he plays. That sets the context to a sports team. In sports, a squad is not the same as a team, rather it is the group from whom the team is picked. The Italian word for a squad in sport is una selezione defined as da cui formare una squadra.
You can be on/in a squad or a member of it, or you train with it, or are picked from it, etc. But you are very unlikely to be said to play with it, on it or in it. So I disagree.
Take a look here http://www.wordreference.com/conj/ItVerbs.aspx?v=giocare The mood you need is congiuntivo