Everyone is getting this one wrong, that's what happens when you ask a legal question in the car repair section.
This is about liability, not about warranty.
Everyone is missing the obvious. I agree with the answers that the labor wouldn't be covered under warranty unless it specifically stated it was covered in the warranty paperwork. Here's the issue, THE ENGINE FAILED BECAUSE OF THEIR INSTALL. The fact is that the company that made the engine might not, let me change that to probably won't, even cover the warranty due to the silly silicone valve cover job. Even if the engine had zero warranty, the shop would have to cover the repair. Even if the shop just did a valve cover on your engine and that caused the oil to leak out, they'd owe you for a new engine, less depreciation. This isn't any different than taking your car in for an oil change and finding out they forgot to put the oil filter in after your engine conked out.
If it's really because they used silicone instead of bolting them down like normal then the failure is due to their work. They'd owe you for a new engine if the engine didn't have a warranty.
That being said, I can't believe anyone would try to use silicone to put a valve cover on a car. It bolts to the head of the engine and that gets very hot while the engine runs. As you've found out, silicone doesn't like heat. If that's actually what this shop did, I wouldn't trust them changing the oil, let alone changing the engine.
If they're not willing to cover the labor I think your best bet to get your car back will be to pay the $300 then take them to court to get the money back. Get good pictures of the silicone that was on the valve cover and it will be a very easy case. You'll just have to go to your local court house and ask what paperwork you need to file a case in small claims court. Don't worry, it's easy, and with your good pictures of why the engine failed, you can't lose. Just by the by, they'll also be responsible for your court filing fees when you win, it's only about $30, but they'll still have to pay you back for it.