I haven't completed the game yet, but can't you get to that transport system? There are several of the zappers that can get you back into the game.

I just completed it (100% minus three hidden achievements) and confirmed you can get back in there. If you didn't unlock the zapper locations at the archives and the grid itself, you can still get in there by just going downt the main power core shaft (the really long one).

I’m having this same trouble getting back to the chess area without having unlocked the teleported before I first left the area.

Any chance you’d attach a photo of “down the main power core shaft (the really long one)”? Still unsure how or where to access it. :-/

I realize this is a few years later, but I came looking for the answer and couldn't find it either. When I did the Grid Clash (chess) mission originally, I did not unlock the teleporter in that area so I couldn't teleport back to it. Now that I've figured it out, I'm back to leave the details for anyone else who comes looking.

The easiest way to get back to the Gird Clash arena if you don't have that specific teleporter unlocked, is to teleport to the "Archives" teleporter. From there, just go into the room on the right, and you'll find the Grid Clash entry teleporter.

When FalseGiraffe mentioned the 'really long' core shaft, he's talking about the 4 vertical shafts in the main level map. If you look on the map, there are 3 tall shafts that are the same size, and one that is even longer. The door at the bottom of that longer shaft connects to the Grid Clash teleporter. To get to that longer shaft, you can teleport to the station called "Power Dome" and then go through the room to the left. When you come out of that room, you'll be near the top of the shaft. If you go all the way to the bottom, then go left a few more rooms (to the 3rd room) and you'll be in the one with the teleporter to the Grid Clash arena.

Legend. Way too long for me to remember what this even was about, but I do remember it's a solid solid game. Thanks for letting others know!