This is something I've wondered myself on occasion because, at least to me, a forum like this does have its own unique appeal. Twitter is not a good place for substantive discussion for multiple reasons and NeoGAF has so many users that if you don't follow a particular topic or thread for a day or two it's impossible to get caught up. Forums like this have the capacity to support substantive discussion on a regular basis while remaining manageable for most forum members, so even if you haven't been posting here for years, there's still a very real appeal to a place like this that you can't find anywhere else. That's partly why I've moved away from posting in a lot of other places and have started to post here a bit more regularly. I still prefer discussing games with other people in places like this above the alternatives and I'd imagine there are many other different kinds of people out there who feel the same way.
What I think it mainly comes down to, then, is the first point Khushrenada brought up. There's a lack of content right now and new users don't really have a reason to sign up and be active on the forums. I remember there was a lot of great forum activity around the time that Xenoblade Chronicles X came out and it was cool to read through that thread every couple days to compare my experiences with the game with that of other forum members who were playing it at the same time. In fact, I think that thread may have been the reason I decided to start posting here more. However, new games haven't really gotten talked about all that often since then. Part of that is due to the types of releases on Nintendo platforms right now. If you love JRPGs, you're swimming in amazing games this year; for me, this will go down as one of the best years in gaming. If you're less interested in the genre though or don't have interest in the particular games within this genre that have been coming out, there isn't much. Talking about new games is a big part of the gaming discussion that takes place anywhere, so removing that from the equation is naturally going to lead to the forums being less active and lacking new content on a regular basis. There are still great posts that are made in the "last game you beat" and "what are you playing threads," so hopefully when the NX comes out Nintendo can go back to a more balanced lineup of games that helps things in this regard.
Beyond that, I think community events and feature discussions are important for driving forum activity as well. Phil's idea for a game night is great and I'll definitely put forth an effort to be part of it (both this weekend and in the future). If that becomes a semi-regular thing, it can be a lot of fun for existing forum members and it may give someone who may just browses the forums from time to time a reason to sign up and start posting. I also really liked the idea behind the "Run the Series" feature. My experience with 2D Mario is limited as someone who grew up with the 3D games, but that topic got a lot of activity and I enjoyed reading the thoughts of forum members who are veterans of that particular series of games. I've put off sharing my thoughts in the Pokemon thread for a while so maybe this isn't the best endorsement for what I'm about to say next, but I think regular features like that are a great way to increase activity and constantly give forum members something to post about. It's difficult to keep coming up with good ideas for topics like that on a consistent basis though, especially when it's only a handful of forum members coming up with the ideas. To that end, I've had a specific idea for a while now and if you don't mind Khushrenada, I'll send you a short message about it later (I would have made the topic already, but I suspect you've already thought about it in some capacity with your Run the Series threads).
I'll share some thoughts on other things mentioned here too:
I do think that having separate Console, Handheld, and General sub-forums is a good way to organize discussion. Console and Handheld could be merged into one (though I like it the way it is now), but you'd definitely need a separate General sub-forum since there are a lot of people here who are multi-platform gamers. Matchmaking probably needs to be its own sub-forum too, or you'd risk just totally screwing any possibility of that happening here. Strategy and Support do seem superfluous though and, while I don't put a lot of stock into these things, I think it does give the forums the appearance of being less active than they really are (and that likely will turn off some new users). Those could be rolled into the General sub-forum or have their own sub-forums in Console and Handheld, but I'm not sure how much work that would be for the people who handle the behind the scenes stuff.
I think you're probably right about cliques Phil, but that tends to happen on any forum. To this forum's credit, I can't ever recall anyone going out of their way to make a new forum member like me feel like an outsider. There are probably ways to make things easier for people looking to sign up like your game night idea or making the new members thread more visible, but in general these forums have usually seemed like a pleasant place to me.