When I was younger I used to develop various modifications for some games and also run servers for them, which I maintained and kept up to date etc. I am now trying to find employment as a System Administrator. My question is: should this be included in my current resume? If so, how would I back it up if asked about it since I have no one to point to for feedback from it.
Even if you have no one to point to feedback, yes I'd included it - but under "hobbies" or "volunteer activities" rather than "experience." That gives employers a little bit more context about what you've done and in what capacity. They also have a way to know that it wasn't corporate/OJT experience, but it is a set of skills that you have, at least for that specific environment.
You also say "when you were younger" - you may want to include a date range with that volunteer-experience, since if it was in the last two years that will be potentially more relevant than if it was over a decade ago.