A SSD won't help you with gaming (only load screens are faster). Your GPU is the bottleneck. Once you get a high end GPU it will be your CPU.
You are correct. Right now his rig is pretty balanced though. An SSD is currently the weak link. Load screens will be a lot faster and you dont get the hiccups you see while gaming if for example your antivirus starts a scan or something like that. I still think SSD but if not, your choice would be my second.