How do you teleport a certain player to spawn after they win a 1v1

Solution 1:

Check for the other person not being there. You can do this by tagging an arbitrary player inside the room (would be the only one if he/she won), then checking if there's another untagged one and then removing the tag again:

/tag @p[x=…,y=…,z=…,dx=…,dy=…,dz=…] add inRoom
/execute unless @p[x=…,y=…,z=…,dx=…,dy=…,dz=…,tag=!inRoom] as @p[tag=inRoom] run <command>
/tag @a remove inRoom

Replace "…" with the lowest coordinates and the size of the room and "<command>" with whatever you want to do with the winning player (for example teleportation). If you want to do it relative to that player's location, add "at @s" before "run".