Although they're getting the first punches to the face because they're easy and obvious targets, companies like Google or Facebook, will trivially withstand it over time. They can afford whatever compliance cost and complexity is involved. It's everyone else that is going to suffer, including all start-ups attempting to offer an Internet-wide service (something that not so long ago could be mostly taken for granted). The effect will be to lock-in the position of the existing giants and protect them from new companies that might challenge their global dominance.
If I want to offer an Internet-wide service in the near future, I'll need to comply with dozens of different Internet-related legal/political frameworks to spread into dozens of nations. It'll be realistically impossible to accomplish for smaller entities, so start-ups will be stuck even more than they already are in struggling to reach beyond their local audiences. This will particularly harm start-ups in smaller countries in Latin America, Africa and Europe. Start-ups in the US and China will gain a further advantage (an advantage which they've already utilized to produce most of the Internet giants to this point), because they get to start out with massive home markets with heavily unified rules and then push to the rest of the world from their large base.
This process destroys the Internet as it has been known the last two decades and it appears nothing is likely to stop it from getting dramatically worse in the next 10-15 years.