I can't really from your explanation what happened for sure. Never disable textdraws/chat when reporting a bug. They could contain useful information. It looks like you won because the player left the server, not because you started moving ! That's why the reason of the elimination is "left".
1. The player was completely desynced and that bug when he can't teleport anywhere happened, so he couldn't teleport in '/duel'.
2. The player was simply paused and he would have been teleported to the duel location when he came back.
Now, if he wasn't in '/duel' for even one second, I think that this is the biggest chance of what happened:
1. His game was being frozen.
2. You used '/duel accept'.
3. You both got configured to spawn in '/duel'. In the first photo you can see him on the radar, because his virtual world got changed, he has the same virtual world as you.
4. Because his game was frozen, his position wasn't updated.
5. His game probably crashed and the server knew that the player "left". It may be just a timeout.
These, or he was simply paused, then opened the game and left the server from the main menu by pressing "Quit Game".
In the next version I took these decision to improve similar problems:
1. You will be able to use '/duel accept' if the other player is in a base. (it didn't really make too much sense)
2. If the other player is AFK/paused you won't be able to use '/duel accept'.
3. If the other player becomes paused while in '/duel', he will be eliminated with the reason 'went AFK'.
These will probably solve this problem, thanks for reporting !