Three pathways.
1. Money is a means of resource allocation. More money, more resources.
2. War of attrition. Raising costs on the other guy makes settling or coming to some sort of settlement more likely.
3. Scorched earth. GS may be trying to send a message not so much to Alyenkov as to any other programmers who'd be willing to entertain a similar stunt. See recent coverage of Amazon's frequent, but nearly entirely unsuccessful, pursuit of noncompetes against former employees.
In particular, bcantrill's comment: https://news.ycombinator.com/item?id=7975428
the fact that we had prevailed against Amazon also gave these engineers the confidence that we could and would do so again -- and ultimately, it didn't prevent anyone from matriculating. It did, however, have one lasting effect: the engineer that was pursued went from thinking fondly of his years at AWS to hating AWS and Amazon with a white-hot passion that still burns today. In the end, enforcing a non-compete is like erecting a Berlin Wall: if you feel you need it, you have much deeper problems...