I understand that my question is very strange because it's evidently that games ported to 2014 year ubuntu will not work for older systems. But i know some users that use very old debian 6 (2011 year) in the 2018 and i think they also play games?

Considering Debian 6.0.10 was released in 2014, I would think that they should.

Might be helpful if you mention what issues you're having with ubuntu as well as which version of it you;re running.

I;m a FreeBSD shop but usually a quick google will help folks.

Linux kernel have perfect compatibility for decades.
Glibc have super good compatibility for years.

Unless you are playing brand new games links with latest libraries, it will not be a (big) problem to run games on old Linux machines.

However, any serious Linux gamer will not play new games on a too old machine.

I corrected that for you...

6.0.10 is a point minor release of 6 and its package base is updated only for security fixes. Yes, linux will work with a game in any version, but new glibc versions very rarely can be not binary compatible with old versions. So, an app compiled with glibc 2.25 will perfectly work with 2.17, but not with 2.16. So in 2018 you need glibc at least 2.17.

No, we don't have hardware compatibility issues, as i see, new games don't really increase in hardware requirements. So, on older systems may be older linux versions.

On a couple of my systems I'm running Mint 17 which is based on Ubuntu 14.04, so far they still play any game I throw at them. Something to be aware of is that the Steam-Runtime (which is what some devs build on) is based on Ubuntu 12.04. Many games should play fine.

I ran 32-bit Ubuntu 12.04 right up to its end of life last year, and don't think I encountered any serious problems (worst was huge installer scripts that I had to manually run with bash rather than with dash, due to the lack of large file support in 32 bit dash (and so that was more a 32-bit problem than an old linux problem)).