The thing in Tetris is the blocks are... blocks. There's a nice bevel that allows the color to go darker at the edge and then there's a highlight at the "top of the bevel." As well as a lighter section right at the top of the square.
These are not just there for no reason. They make it much easier to see over diverse backgrounds. Even if we sample an exact color (in this case the Cyan) we can still see the Cyan blocks because of the dark and light edges:
While I wouldn't suggest anything that bright, if we adjust the lightness we can quickly see how easy this is to match (all I did was drop the Lightness):
Likewise nearly any dark color could work:
The darker or lighter you go the easier it is to see, and people don't generally like looking at bright things but it does work both ways:
While going almost but not quite to black so we can still have some color:
That bevel and emboss is what really allows you to use any background color. So yes I would say add them and then you can use pretty much any background you want.