Latency is the factor determining whether it will work on SAFEnet. This paper looks at this subject across a range of different types of online games: http://web.cs.wpi.edu/~claypool/papers/precision-deadline/tr-06-13.pdf
This graph from the paper is a nice tl;dr. Note that “FPS” is the abbreviation of “first-person shooter”, which is closest to the laser tag type of game.
The blue line intersects the lower limit of the grey zone at a latency of 108ms, which is the benchmark such a game will need to aim for.
I looked up some statistics (scroll down to the second table) on latency between different parts of the world. Bottom line: latency within countries is usually very good (Intra-Japan at 9ms) and for regions is roughly at or below that cut-off figure of 108ms, but on trans-oceanic hops (e.g., Australia-U.S. at 153ms) generally exceeds it.
So, with the multiple hops of a SAFEnet route between unpredictable places anywhere in the world, you won’t be able to achieve acceptable latency with a purely SAFEnet solution.
I imagine (correct me if it’s otherwise) that that laser tag game operates on a local network, a wireless LAN, while your SAFEnet neighbours, such as the other participants in the game, can be anywhere in the world. On the other hand, there might be ways to mitigate this by doing the setup on SAFEnet but the action on a local, clearnet channel, as with my idea of obfuscated file transfer “obfuscated file transfer”).