What could possibly go wrong with running precompiled binaries that were linked to a set of precompiled libraries with a completely different set of precompiled libraries.
You're not wrong, it's definitely not something a n00b should attempt in most cases. But I've done this before to save myself the need for distrobox. A lot of proprietary software only offers .deb, but is usually either statically linked or comes with its own set of nearly all the libraries it needs. So just extracting and running it often does the trick on non-debian distros like Fedora in my case.
Seriously though, just use distrobox or see if there's an unofficial package for your distro that you trust (AUR/copr/ppa/OBS). It's more straight forward especially if you don't know what you're doing.
Not the locations. The versions. Your libssl-1.0 isn't the same as mine. There often are differences in major, minor or patch versions. There even are differences in compile options where a feature present in one is not compiled in another. E.g. ciphers available in libssl.