Google is actually right here for once. Signal is not offered on F-Droid, and its package name is org.thoughtcrime.securesms, not org.thoughtcrimes.securesms.
Only official places to download Signal are through the Google Play Store or their website (which self-updates).
Yeah, anticheats are a privacy and security nightmare that most people don't even think about. You're effectively giving their proprietary software extremely invasive kernel level access to your system. They can access and do pretty much anything they want on your device with really nothing stopping them. Anticheats like this are extremely dangerous and should certainly be avoided where possible.
I understand the problem of cheating in games, but I feel like there has to be a better solution to this problem, as making users install an extremely invasive rootkit isn't acceptable at all imo. I'd recommend avoiding games that include invasive anticheat or DRM like this. Best way to get across that this isn't okay is through the wallet.