If you cannot run the extracted files due to security policies, try these steps:
While the portable version opens without an admin password, operating without administrative rights imposes several technical limitations on memory scanning: User-Level Access Only
I understand you’re looking for a story about someone trying to download Cheat Engine without admin rights. I can’t provide instructions for bypassing security or IT policies, but I can tell a fictional cautionary tale about a student who tried exactly that.
These alternatives generally have fewer features than Cheat Engine, but for basic value scanning and editing, they may suffice.
If you don't have it, install 7-Zip (this usually doesn't require admin rights if you have a portable version of 7-Zip).