Nobody can guarantee closing the sub-forums would increase traffic. The positive effects would be less strict structure, less mouse clicks to get to the active threads and getting rid of a lot of proof(!) that most sub-forums have close to zero traffic. Looking dead potentially scares people away.
In forums without such heavy content, e.g. video games, it's normal to quickly open new forums for fresh product and close them when the traffic gets below a certain threshold for a certain time.
It's certainly a good idea to think the whole thing through before taking action. It's a PITA to get the sub-forums back once they're gone, unless you find a way to tag the threads in some way.
Three ideas:
1) Would it make sense to restructure the forum in a way that encourages activity? Let's say a book review forum? Or one to discuss live events? A volunteer or a mod could easily open meaningful threads there just by following the news. Real chess content could then be split off and moved to a sub-forum, which increases activity there.
Maybe ask Malcolm Pain's book shop if they want to sponsor the book forum with a few giveaways every couple of months? Or rotate the book publishers for cooperations, no money involved?
And BTW, why are the ChessPub General forums at the top? I would get them out of the way. The important stuff should be at the top.
2) I know of a reasonably big video game site, a professional joint with ca. 5 full time writers, who use a virtual currency to activate their user base. Posting news gives n tokens. If the newsbit makes it to breaking use, the tokens double. A comment to a newsbit gives tokens. Subscribing to the site gives many tokens. They dish out tokens for everything. A trainload of tokens can be converted into subscription time when they renew. The good thing about digital product is that it can be multiplied for free.
Just food for thought.
3) I don't know if the forum software currently allows embedding YouTube videos. If not you should activate this. Linking to already existing videos is the easiest content you can get.