I haven't tested that much yet. If not ICMP, what kind of traffic should be prioritized for online gaming? Just ordinary UDP/TCP traffic on specific ports?
Prioritising ICMP by itself probably won't make much difference. It is only a "control" protocol - a ping is just one of the message types (Echo). ICMP exists only to allow the two ends of an IP communication to exchange status information.
A better approach is to prioritise small packets of whatever protocol. VOIP in particular but also typically gaming will only use relatively small packets, whereas bulk downloads will use the full size the end to end link supports.
The simple way is to limit the maximum throughput on your upload (and if you have a decent ISP they should be doing the same on their end for the download) to just below the sync rate.
Full QoS rules would use different queues for different protocols but games in particular use a pretty random selection of ports and protocols so simply prioritising smaller packets is probably the best you can do.
Doesn't the ping reported in games actually mean anything in terms of sending and receiving data to the game server?
Unlikely. Some games may use the ping to choose which server you are connected to, but the actual communication won't use ICMP.
I did find that prioritizing ICMP traffic helped with pinging websites (preventing dropped packets during file downloads), does this have any real impact on Internet usage?
No, what you found was that prioritizing ICMP traffic helped with not dropping ICMP packets. Other packets may have been dropped instead of the ICMP packets.