No, the EU is not acting this way because they want an "EU Apple". Nobody over here has the illusion of any such mega corporation ever coming out of the EU. The IT industry we once had was killed mostly by price dumping from China in the late 2000ies.
Those mega-corporations are solely coming from non-free regions. If there is someone right now starting to massively take away market share from US mega corporations, then it's Chinese mega corporations.
The EU are doing this because they wish to protect the basic rights of their citizens. Well, and they are not purely doing this out of their own - a small number of hacker activist for the last couple of years have sued pretty much all EU institutions to make them enforce the laws we have here.
I would recommend you check out the very first three words of the US constitution again. Spoiler Alert: It's not "We the oligarchs" :)