Originally (TW2002 v1, early 90s) the game actually only allowed a single player at a time. Most hobby boards only had a single phone line anyway, so this wasn't an unusual restriction compared to other bbs doorgames of the time.
The first "multi-node" (simultaneous player) version was the MajorBBS/WorldGroup port of the game in the mid 90s. These BBS's were typically pay-to-access since they had many phone lines... not to mention the bbs software and games were way more expensive for the sysop to purchase.
The normal doorgame version (non-mbbs/wg) eventually had multi-node support too, but not until the late 90s. I vividly remember being blown away when this came out :) Most normal doorgames didn't offer this level of real-time interactive gameplay, as it wasn't easy to implement correctly in the confines of a 16bit DOS application. Each player had their own process running, and the door author had to figure out coordination/locking/IPC using just a few primitives such as shared files.