People wishing to create simple solitaire games will tend to look elsewhere, since DM is a language which demands at least intermediate coding skills for good results, and there are many game creation systems available with a simpler learning curve to tackle before achieving satisfactory results.
Of course, there are good reasons for creating solo games in BYOND. However, BYOND opens the opportunity for a type of hybrid game which combines elements from both traditional single player games and the ability to support multiple clients. I will describe several possibilities and suggestions, in the hope that someone gets inspired to create a game with a differant perspective.
The Spectators
The most basic way of adding multiple players to a single player game is by making every player beyond the first a simple observer. Observers would have no influence on the adventures of the main player, but remain passive spectators. Depending on the wishes of the programmer, the spectators could communicate with other spectators, or even with the player... but that leads to the next level of interaction... The Voices.
The Voices In Her Head
By allowing the spectators to communicate with the player, you will give them indirect control over the game. Of course, the main player doesn't have to listen to the voices in his head, but it may be of advantage to him. By giving the spectators ability to know more than the player, for example by allowing them to move around on the playing field to spy power-ups or enemies outside his line of sight, they could give him tips and tricks for survival... or even lead him astray.
The Enemies
One possibility, especially in RPGs, is for spectators to "take over" the role of NPC monsters and enemies the main player meets. Whenever combat begins, control over the mob can be given (or auctioned) to a spectator who will try to do his best to defeat the player. This can liven up combat situations by adding the "human element" to tactics, without having to make an RPG a multiplayer game.
Multiple Personalities
There is no main player... all players are personalities in a single body. Control over the body is either peacefully divided among the personalities (by voting, or having turns), or the egos combat each other for an opportunity to use the body. Especially combinations with a "black soul" amongst them can become very exciting. And this provides a basis for a continously hosted game, since it can simulate personalities growing dormant and suddenly forming as people log in and log out.
You can even go one step further, and give each player control over a single limb, or a sense organ, and force them to work together in order to achieve anything.
The Hybrid
Most multiplayer games on BYOND are based on the concept that all players are created equal - but by dismissing this guideline and making a single powerful player and setting all others to the position of "aides", you open a whole box of possibilities. Sometimes it's nice to have someone do all the hard work for you.
And to flesh things out, here are two concepts which wrap some of these ideas in playable form.
Adventures of Thorgard the Barbarian
Formed after a television concept, each game session is an "episode" several minutes long. The spectators can not communicate with Thorgard, but they can show their approval by "booing", "applauding", or providing a laugh track at the barbarian's antics.
At the end of each episode, the spectators vote on the episode's quality, and low ratings will probably cause the next episode to have more senseless "sex" or "action", like raids of cheap extras (orcs) and if the ratings sink too low, the show is cancelled. However, if the ratings are high, the show will afford higher quality "CGI" monsters and better treasures... so in effect, the "acting" of Thorgard and the tastes of the audience will affect how each session is randomly generated.
The Gods
Each spectator is a small spiritual being with a certain area of influence, such as rain, earth, life, and so on. They can affect the elements of their domains with spell-like effects, but only when they have enough spirit energy. And, unluckily for them, the only way to gain spirit energy is by receiving prayers from the main player.
Optimally, the spirits would fight amongst themselves to become the prime "god" of the player character, each promising him the best delights if he would only worship them, or try to punish the player with their residual power if he doesn't.
The second game that comes to mind is one of my all time favorites, Silent Service, also for the NES. This was a single player submarine game which made use of both joysticks when viewing through the periscope. Instead of switching between the two joysticks, we'd just play as Captain and Navigator, and blast those destroyers out of the water. :)