it depends on the games drm, some will allow you to play your games on multuiple devices. origin and steam both allow it as you have to sign into your account to play. so yes in respect to games from origin.
others may not though. some ask for a key and then 1s its registered if its found again and is attached to a different motherboard mac address the game will work on the new install but the old will become invalid. then its a case of how many times the game is allowed to be registered without the key being perma blocked.
by the way, is it free to download the game?
if i buy the game from origin and download the game onto the device, wouldn't I have to buy it again just to download it again? because some places don't give you the disk but only the download file with a serial key.