The easist thing to do is check for the file in an online repository search tool.
https://pkgs.org/ is the one I use.
You said you use Debian / Ubuntu so apt-file should also be an option for you. (Although that will only search the repos you have enabled.) The Debian package tracker should also be of use for you.
(packages.debian.org) That being said, just copying the .so files like you would copy .dll files on a Windows installation isn't recommended. Most likely it won't work. Either due to broken paths, distro specific customizations / patches, or missing resource files. Remember this is Linux. Backwards compatibility is not really a thing here, and even if you manage to get the needed .so files in the correct places, there's a chance the libc they need will be incompatible with your kernel.
You also shouldn't install a random older repo. That can break your installation pretty badly if your package manager doesn't catch it.
In my personal opinion grabbing the Windows version and running it through Wine, or getting some other version working in an emulator, is a far better means of getting games working (and preserved) under Linux. Instead of hoping that your Linux native version will run 10+ years from now. Just try getting some of the older ID Software / Epic Games ports running if you don't believe me. UT:GOTY works far better as a Windows app under Wine than the native Linux version does on modern distros.