What games for time-poor, casual gamers & writers on rpol?
In my experience, the system doesn't matter so much as the way it's applied. Even something as potentially time-intensive as GURPS can be done on a very casual basis, as long as everyone involved is in agreement on it.
Someone mentioned freeform earlier...since you specifically mention writers in the subject, I assume you've got some interest there, and if you're in the right group, freeform is a great way to develop your writing, as there aren't any dice and very few rules to help guide the story...it's all in the hands of the players and how well they convey the story. It is also, unfortunately, easily prone to abuse unless you have a GM who's willing to ride herd on people who are trying to redefine the game to fit what they had in mind (that long-running game I mentioned has had that happen several times through the years, where players took the lack of posted guidelines strictly delineating what is and isn't applicable in the game, and tried to re-write what the game was going to be based on their ideas...a couple of guys still try it every now and then and the GM has developed a lot of experience with saying "Nope.")
Any game, regardless of system, can choose to focus on story development...but in my admittedly limited experience, a lot of dice-based-system games get caught in the trap of 'you'll have to roll for that'. While I enjoy a certain degree of randomness in my games (because I'm one of those weird gamers who doesn't like to assume that my character's success is always a foregone conclusion), there comes a point where the dice, while technically applicable, are taking away from the story...and the story is my favorite part of gaming, whether I'm playing freeform sci-fi or Shadowrun or Star Wars or Burning Wheel or whatever other system you want to put out there.
Which kind of drifts off my point, but in a way also underscores it. The important thing is how the game is being played, not so much what rules you're using to play it. I've been in tabletop groups where the rules were hardly referenced, I've been in groups where almost everyone had their own copy of the rules so we could look up how to do the attack we had in mind and explain it to the GM to try and keep things flowing smoothly. I've been in groups that played multiple times a week (in college, for a few years, I shared a house with several people...we were all gamers, and there was something being played almost every night) and I've been in groups where we met maybe once every other month and played for a few hours (a couple, really, once we got through all the 'what have you been doing lately?' conversations). They were almost all fun, even the GURPS game where we were all wizards' familiars and the GM got a basic concept from each player and built our characters for us...the game itself was wrapped up in maybe three or four sessions. In none of those cases was it the rules that made it fun (although there were a few times that the rules made it not-fun...my old tabletop Star Wars group died, in part, because we changed from the D6 system to the D20 Saga Edition rules, and they so totally bogged down play that after a couple of sessions, nobody had much enthusiasm for keeping the game running...that was a group that played, in various incarnations, for almost 20 years...)
Look for games that have a slow posting rate expected, and a setting that really appeals to you. Then, worry about whether or not it's a system you know (or are willing to learn.) That's how I would do and have done it.