There's probably a way of making these switches for less, if you're willing to trade money for toil and strife. Wind up toys have a very long roll of "wind up spring". 3D print a jig to bend a short piece of that into shape. Use somewhat translucent filament to print the switch. Or use a diffuser/matte thingy from a LCD monitor. I don't know. It'll probably be more expensive in the end but you'll feel good that you did it.
The remark about a touchscreen amused me, since this is essentially a lo-res touchscreen. You can have a super high resolution full color touchscreen for small moneys, but if you want it to be super low res and monochrome you have to pay big moneys and you also have to design and assemble it yourself! In a way this is obvious, but it's also kind of bananas: you can only easily do things that are popular. Then again I suppose there'd be no project if it was easy.
I can't put my finger on it, but there's something very satisfying about seeing his final build, that I think wouldn't be there if it were a touch screen.
with a small amount of additional memory the display could hold the game state and you could manually flip the dots to input the cells.
Much more scalable in cost.
$3*17*17 = $867 - ouch!