I was there in 1998 (and a couple of times in 2006 although I didn't have time to check out the shops) and there was at least one game store at the time but I don't recall the name or exact location. (And, yes, this makes my post next to useless but please consider it a friendly "bump" because there is at least one person on this site from Cairns. In fact, I am sure this question has been asked before.)
If you haven't been to Oz before, be aware that things are quite expensive especially now that the AUD and USD are of roughly equal value. Average salaries in Oz are a lot higher than in the USA (AUD65K is average) and there is not as much competition due to a really low population for a country the same size as the continental United States (and high transport costs for imported goods also inflate costs).
Cairns is about 2,000 kms from the nearest major city (Brisbane). And like [MENTION=21843]Dioltach[/MENTION] said, wildlife can often be described as "real-life monsters". Beware of all snakes and spiders. Australian snakes are roughly the deadliest in the world and the spiders are not far behind. Not all are venomous but pretend they all are unless you really know your stuff.
I was also warned on my last couple of trips there to beware of roaming gangs of street kids. Even if they're half your size, stay as far away from them as possible. (It was rather ironic that I was given this warning because I was in Cairns simple to avoid staying overnight in Port Moresby which is one of the most lawless and violent cities in the world.)