I've never had a complaint or issue with a dining table cover on a poker table. Providing the rail is made with good quality material, and the padding is high density and also good quality, there shouldn't be any signs of damage to the rail. As Irish mentioned as well, the weight is distributed quite well over the surface area of the rail which prevents any heavy spots on the rail to cause any damage.
Depending on the design/options, sometimes a dining table cover can have a bit of wobble because the wood top is sitting on top of a padded surface. If the rail has no cup holders, then it's sitting directly on top of foam, so if you push down on a corner, then the foam underneath will compress a little. If you have cup holders in the rail, and the cup holders are sitting on cup holder rings (or the cup holders are tightly pressure fit), then the topper is sitting on a rigid surface so you don't get that problem. The table legs can also contribute to the wobbliness of a table as well, but if the poker table has a solid base, then there shouldn't be any give.