At least for my own country, if you buy advertising from Google, you pay 0% VAT because it's not a local purchase. With a local company there's 18% VAT. The local companies are starting the competition at a huge disadvantage.
An even playing field is a healthier market, without megacorps that can run at a loss for decades to crush out any chance competition in a field.
If you do business with VAT registered company from different country, you do not pay VAT upfront with purchase, but you report it at the end of quarter (monthly if you are big enough). You will actually never pay this VAT if you are VAT registered company as you will report it and ask for refund at the same time.
On the the other hand, if you are doing business with local company you pay VAT with payment for service or goods and ask for refund at the end of quarter. Long term cost is same, but it blocks your resources (paid VAT) and it may be difference for some companies.
How is prejudicially taking money directly out of the market "pro-market"? Anti-globalist I'd maybe grant, but since the tax is universal, I think it's pretty globalist as well.
They're in fact assisting in the beginning of an economic war between the US and the EU. These taxes, intentionally and specifically targeting critical US companies, are de facto tariffs. The US will have no choice but to respond in kind.
There's no scenario where Germany doesn't get its export machine hammered with tariffs if the EU broadly goes too far with this. It will drag the EU economy below water into a perma recession (which it has almost been in already since 2007, all the major economies of Europe have seen near zero net GDP expansion for over a decade). Europe is extraordinarily weak, with Brexit and France, as well as the continued residual mess in Spain, Italy, Greece and Portugal from the great recession. Germany is the only thing propping up the EU economic house of cards. And that's what the US will target to break the back of the EU. If I were the US, I'd start with finishing off the collapse of Deutsche Bank (down to a $16b market cap now) and move to decimate their auto industry (conspire with China as it makes sense, we can carve the world in half between superpowers; they'd love to take the place of some of Germany's advanced industry and move up the ladder of development further). Once it's war, it's war. Or you know, the EU could be smart, turn back and stop the targeted assault on the US economy.
If it gets really feisty, just look the other way, Russia will begin rebuilding its empire by consuming parts of Eastern Europe (which it's always desperate to do). That will destabilize an already weakened EU. These countries are either allies of the US, or not. If they are, they will stop attacking the US economy. If they're not, I don't see why the US should be protecting them from Russia with its military power. And there's absolutely nothing the EU can do to stop Russia from taking what it wants in Eastern Europe.