Call your jurisdiction's plumbing inspector and ask him to swing by and tell you whether this is to code. Presumably, a professional contractor charging $50K to do a renovation will have obtained the appropriate permits...
And never believe it when someone who has a dog in the hunt (i.e. something to gain/lose) tells you that something is to Code, unless they are a top-notch professional recognized as such in your local community. Every hack will always tell you that the crappy job they are doing is "to Code".
If my fabulous licensed local plumber Jim Brown tells me that it's to Code, it's to Code. That's why he gets a lot of money for his work, and I know the pride he takes in doing things absolutely-correctly the first time. If the guy who is a "plumber" who is a friend of the gardener tells me that, naaaah.
I also don't know why people take such crap from contractors. YOU hired this guy. Presumably he gave you plans or drew plans for the permits or at least gave you a contract that said, "Install Island Sink, including loop vent and drainage" or such. Presumably, you haven't paid this guy yet. If he refuses to do it right, and apparently he originally told you he was doing a loop vent, fire him and don't pay him. And get someone else to do it who will do it right. You're not a prisoner. You have his money in your pocket (at least you should).
It may be that what he is doing is correct or acceptable in your jurisdiction and that is enough for you. You should find out for sure, from the local authorities. If it isn't, then it's up to you to take action.
Frankly, that you're telling me that the "contractor" is doing the plumbing raises all sorts of red flags for me. When we do stuff, we have the plumbing portion done by a licensed plumbing contractor, and we have the stuff inspected.