As would anyone else, outside America. That's not the issue anyhow.
Blizzard would just set up Russian subsidiary and sue them in Russian court with Russian court orders.
However, the bigger (and the real) problem is that Russian anti-piracy and copyright protection laws are toothless and the operator are well equipped to circumvent the injunctions. It's hard to prosecute and shut down illegal sites in Russia. We might not even have a global ransomware problem if Russia took this seriously, but since their political stance is pro-coldwar, they won't - all this stuff disrupts the west and that's just fine by Russia.
Nostalrius running in Russia is just a piss in the ocean compared to the grief that part of the world is causing the Internet infrstructure and everyone in it.