multi computers?

[Zukum]

i bought Don't Starve on my pc. and i wanna play it on my laptop. i can play it on my pc but the colours are all funny (blacks all come up as reds) so i figured i would play it on my laptop. it shows up when i open my chrome browser in my extensions, and when i start it up it says play demo and buy now or enter product key. my chrome is synced, where do i find my product key? or how can i sync it up so i don't have to? also when i open my browser and go to options then where it says signed in as the extension tab don't starve isnt showing up there