Since it's a start-up, it's most likely that their lawyers just drafted this up for them, and the founders don't really know any better. Lawyers tend to be overly cautious this way, but entrepreneurs usually realize that running a business takes some risk. If they really want to hire you, it's likely that they'll be willing to change the terms. If they're not, then this is what should raise the red flag for you...

In any case, if the contract doesn't feel right to you (as it should) and regardless of whether it's enforceable or not, don't sign. Why put yourself in a position where you are likely to have legal issues in the future?