No, DVC owners are not eligible for free dining or any other resort/room discounts from Disney. Disney has their business not matter what, they aren't giving them extra discounts on top of their DVC ownership. Free Dining is probably the reason we won't ever buy into DVC or even rent points. For a family our size, I believe, it's a minimum of a $25,000.00 buy in to get a villa the size we need. I haven't hardly spent that much money in 7 years worth of free dining trips. And as for renting points, it's double the cost of our vacation, as opposed to staying in 2 connecting rooms at a value resort with free dining.
Now, don't get me wrong, the DVC villas are very beautiful and most DVC owners love it, you just have to run the numbers to see what works for your family. If you have a smaller family and do a lot of your own cooking, the villas can be a great option.