The US heavily invests in using video games for propaganda and ISIL and Sunni-insurgent forces have been exposed to a number of anti-Assad video games. Hamas is unlikely to be the progenitor of anti-Assad video themed video games. It's speculative, but it makes a lot of sense that the US would do what it can to direct ire at Assad.
What's not speculative is that Turkey and the US were running guns to groups that became ISIL factions in Syria.
There's lots of influence to be had all over. The larger powers are trying to manage the situation to achieve their ends. That means funding insurgent groups where it benefits them and bombing the same groups from the air where they are challenged.