Is it possible to build a computer that can play
ANY type of game, REGARDLESS of the age of the game --
fast OR slow --
one computer that would cover it all, whether the game is on
disc or online;
If you're looking for a computer where all you have to do is stick the disc in and go, the answer is no.
If you have technical skills, or are willing, able, and have the time to learn the technical aspects, you can get MOST older games (not all) working on a modern computer.
Other folks here have mentioned the emulation and virtual machine software that can be used to play old games. I won't repeat, except to say even the virtual machine solution can be limited in the cases of Windows games that have speed issues (1997 version of Safecracker) and early Windows games that require 3D-accelerated graphics.
However if you're looking for a "stick the disc in and go" computer, which is how it often worked back in the Windows 95/98 days, it's not possible for games of all ages on a new computer. You can get that (or something close to it) once you've set up the game, but the method for installing different games will vary depending on the operating system it was made for.
I'm not going to go into new and upcoming games, but game requirements are a moving target, especially for "the latest" action games. Adventure games tend to have lower requirements, a few years behind current action games. Compare the requirements for the new "Witcher" game with the requirements of "Book of Unwritten Tales 2."