The EU doesn't want big tech out. It wants big tech abusers out.
And guess what, most of those big tech abusers are American.
But if it helps with anything, it doesn't look too kindly upon Chinese companies, either.
It can't really do much about European big tech companies since there aren't that many left... and they're in enterprise markets where things work completely differently (enterprises can sue you themselves very efficiently if they're disadvantaged, thank you very much).