Neoliberalism is about having faith in the incredible power of competitive markets, which have transformed human society and progress in the last couple of centuries. But not all markets are competitive - and private actors will always have private incentives to impede competition and create monopolies, and occasionally will encounter the opportunity to act on those private incentives.
Neoliberalism isn't libertarianism. I think neoliberals generally favour state intervention when that's targeted at correcting market failures where private and public incentives otherwise become misaligned (for example, introducing carbon taxes).
Aren't non-compete clauses inherently about stifling competition? My instinct is that this is just about promoting competition and the power of the market to do its thing.