These types of programs use published Windows API to survey executing tasks.
They may also do DLL injection
to incorporate their own code into executing tasks and access their memory,
or Hook Windows API functions
invoked by executing tasks and examine their parameters or block them.
Once installed, such "spyware" is unstoppable. Games that use it may refuse
to run if that software is somehow uninstalled or blocked.
Running the game in a virtual machine may isolate it from your
running system, but performance may be impacted or become impossible.
The best advice is to do nothing - if the game is distributed by
a respectable company, it is highly unlikely
that it will exceed its assigned functions.
EDIT
There have been some reserves about trusting well-known companies,
citing the 2005
Sony BMG copy protection rootkit scandal.
That case has helped in drawing specific red lines for the industry
which it will be very costly to cross
(as Sony has learnt).
However, the Sony scandal is nothing compared with the 2011
RSA Hack
(recommended reading) and the
2020 United States federal government data breach.
These have shown that any software can be compromised,
either by direct attack or via indirect one via its
software supply chain.
Today, we can only deal with probabilities: It's highly probable
that any respectable company will do its utmost to protect its product
and avoid any scandal. It's also probable that there is some weak link
in its defenses, whose effect depends on it being exploited with success.
We must trust something, or we can stop using software.
We have to trust some companies, as we don't really have a choice
in the matter. All we can do is keep our defenses up with antivirus,
firewall and more, keeping good backups for the case that the worst
would happen.