Not quite… in the most common version of chessboxing it’s more a case of alternating between the chess & the boxing via, say, a 3 minute timer from the start of each “round”. You do need to be very careful moving the chess board in/out of the ring between rounds so as not to upset any of the pieces but otherwise play just continues round by round until checkmate or knockout (or TKO or a clock falls etc.)
Source: I fought in (and won!) a one-off chessboxing exhibition match in London back in 2012
It's just a completely different paradigm of rendering and it's not clear which one will be dominant in the future. Gaussian splats are usually dependent on initialisation from point cloud, which makes whole process much more compliacated.