Yes the Fettuccine Alfredo is vegetarian.
The Fettuccine Alfredo is considered vegetarian and contains freshly grated Paramesan and chopped chives.
Some Fettuccine Alfredo dishes have added chicken to the Fettuccine Alfredo which would make the Fettuccine Alfredo not vegetarian.
But if you order a Fettuccine Alfredo dish without any meats then it is considered vegetarian or you can also order the Fettuccine Alfredo without cheese but it's less delicious that way.
When you eat cheese or meats the food is not really considered vegetarian because the milk that makes cheese comes from cows.
And vegetarians don't want to eat or drink things form animals.
But if you make or order the Fettuccine Alfredo without cheese or meats then it would be vegetarian.