You can make any kind of game, as long as you do not steal any sprites, music, etc. from other games that you are not allowed to use.
Also, the time could be any you can think of, the pong era where only a few pixels where able to be displayed, nes where more complex sprites where able to be displayed, playstation where the first types of 3d games where developed, early xbox, etc. As long as you use a noticeable element from the past (like low pixel gfx) then go for it! ^^