If you have a key, they can monitor your usage and make sure that everything is copacetic -- you are below request limit, etc. They can separate their stats on regular vs API usage. If they are having response time issues, they can make response a bit slower to API users in order to keep the main website responding quickly, etc.
Those are the benefits to them.
The benefits to you? If you just write a scraper, and it does something they don't like like hitting them too often, they'll block you unceremoniously for breaking their ToS.
If you only want to hit the thing a couple of times, you can get away without the Key. If you are writing a service that will hit their feed thousands of times, you want to give them the courtesy of following their rules.
Plus like Dave Webb said, the API is nicer. But that's in the eye of the beholder.