however you will see that even a slight ability to chose the games which you use as a representative entirely changes the results
With respect to working out if old games are better or new games are better, being able to choose representatives does indeed completely change the results - it invalidates them. Anyone who thinks old games are better and new games are worse (or vice versa) is more likely to pick good old games and bad/aveage new games (or vice versa).
You see in chosing completely at random you actually introduced an entirely different bias. It is the equivilant of saying that "France has terrible food because I went outside and pointed at random objects and most of them tasted terrible".
No. You could say "France has terrable tasting objects" if you did that. You introduce a new selection bias if you do that to measure the quality of food (by selecting objects that are not even relevant). In my example you are selecting random games to measure the quality of games. In your example you are selecting random objects to measure the quality of food.
What I am trying to get to is that the "plenty of games" you have
are the exception.
There is someone on youtube (ZetaPlays) who is trying to play every single NES, SNES and genesis game made, and he uses a program to select them at random. Most of them are terrable, and it gives you a perspective on earlier gaming (consoles in particular) that many people who grew up loving their NES would never see, the "dark side" of their favourite era of gaming. It is quite interesting.