Fix it!!

if the system says he has the game, but he hasn't - it's a glitch in SG's system and it needs to be corrected? what don't you understand about that?

on the contrary - i would believe it is a "communication error" between steams database and SG, seeing that there is a F2P version SG's database would be likely to mix the two up

You need to wait untill it won't show on Steam the game as recently played.