And today we read from the Book of Sony, Chapter 2005, verses 10-11: Sony BMG quickly released software to remove the rootkit component of XCP from affected Microsoft Windows computers, but after Russinovich analyzed the utility, he reported in his blog that it only exacerbated the security problems and raised further concerns about privacy. Russinovich noted that the removal program merely unmasked the hidden files installed by the rootkit but did not actually remove the rootkit. He also reported that it installed additional software that could not be uninstalled. In order to download the uninstaller, he found that it was necessary to provide an e-mail address (which the Sony BMG Privacy Policy implied was added to various bulk e-mail lists) and to install an ActiveX control containing backdoor methods (marked as "safe for scripting" and thus prone to exploits). Microsoft later issued a killbit for the ActiveX control.

On November 18, 2005, Sony BMG provided a "new and improved" removal tool to remove the rootkit component of XCP from affected Microsoft Windows computers.

courtesy wikipedia: https://en.wikipedia.org/wiki/Sony_BMG_copy_protection_rootkit_scandal#XCP_rootkit

Depends on what you uninstall. Your OS? Yes. The game? ¯_(ツ)_/¯

I don't know but if you get a law degree then spend 3 months reading their extremely long and intentionally complicated user agreement I'm sure you'll find out that they have the right to keep it installed whether they currently choose to or not.