They play in Serie A. Serie A the Italian league. Inter is Italian.
The nationality of their players does not matter. There is a reason that we have international football and club football.
In international football you represent your country. In club football, you represent a club, a district, and the city that you live in along with all the supporters of the club. Whether you are fit to do so or not depends on your qualities - nothing else.
The people that you represent, in an Italian stadium, are mostly Italian. Whether this has any significance or not, I'll let you decide.