I don't think this has anything to do with working harder. The startups are working on the weekend because they are succeeding, they aren't succeeding because they are working on the weekends.

When you are in a startup that has found a market, and all you have to do is ship the next MVP and you can start printing money, you're pretty motivated to work weekends to make that happen faster, even if it's a bad idea.

I would guess that these successful startups could stop working weekends, change their culture to focus on measuring value and deliverables, and still be successful.