weird just try setting the "Minecraft lancher.exe" in and rename it to "minecraft.exe" and see if this works
i had the same problom yesterday off me writing it but if it keeps just saying install it's because twitch does install it at where you have selected that it should install
it is in (where you have installed it)Twitch\Minecraft\Install
the "minecraft.exe" file in the folder is corroupt
you can delete that and replace it with a copy of the Minecraft launcher just remember to rename it to "minecraft.exe"
ps. if you have any questions i will be here the next few days to try and help others with the problome