As someone from a family of very very proud, very loud Italian-Americans, it pokes fun at them pretty well.
Italian-Americans, especially in the New York and New Jersey, are their own distinct subculture, almost completely separate from actual Italians. Think of the difference between a French person and French-Canadian, then triple it.
Half of that food in the commercial isn't even traditionally Italian, it's from the Italian-American diaspora. Chicken parm was invented in the US - a friend of mine from Italy loves it, though, and literally described it to his parents in Italy over the phone once (They were intrigued). Same with scampi, marinara sauce, many others. Garlic bread was an improvisation on bruschetta.
Your average Italian doesn't even know who Christopher Columbus was, let alone give a shit about him, but Italian-Americans do. Actual Italians don't pronounce capocollo "gabbagool" or drop random letters from other Italian foods ("mootzarell", etc.) or call sauce "gravy".
Like I said, I come from a heavily Italian-American Jersey family. I think the subculture is kinda silly and doofy so I couldn't care less about it, but I imagine some Italian-Americans might take offense. Actual Italians would probably be laughing too.
The Sopranos really poked fun at this phenomena when they sent them all to Italy.