If by "purchased DVC points" you mean 'rented from a DVC owner' -- yes, if you are staying at a DVC resort, regardless of how you got there, you should be able to use the Community Hall associated with that resort. (If you meant something else, I'm totally confused.)
I do not know if you have to be a DVC member to use all of the services for free, but even if you have to pay a fee it's pretty reasonable.
The Community Halls usually have games and books and craft sessions every day. DVC members (and, possibly, those who rented from a DVC member) can check out DVDs for free and those people paying in some form other than points can rent them for a nominal fee. I think there are usually bicycles to rent there. Board games and books can be taken back to your room; I've never checked out any Community Hall other than Boardwalk's, but BW has a couple of computer game stations and a pool/air hockey/something like that in the middle of it. I would not be surprised to discover that you can rent tennis supplies there, either.