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
Source: I fought in (and won!) a one-off chessboxing exhibition match in London back in 2012