US tech giants haven't worried about competition coming from Europe for awhile now. They worry about competition coming from either within the country or China.
A distant third problem are US regulators, which are slowly moving forward with targeting the tech giants (which now has both sides of the political machine looking at them, for different reasons). The giants no doubt feel like they can massage that situation better, as it's their home turf. They're invasive aliens as far as the EU is concerned.
How would the EU block them? This is especially important if the Russian or Chinese entity has no locus or presence in Europe.
(for instance, would you be able to get around it using a different DNS, or by using a VPN?)