I am not familiar with the jenga game, so I am not able to picture the blocks.
A table saw with a decent blade can cut wood to a very smooth feel.
If you are not able to cut to the desired smoothness, then you may end up needing to apply some product to fill in the roughness of the wood.
Take a look at SlipIt. One of several options.
http://www.woodcraft.com/product/2004247/9013/slipit-jell-1-pint.aspx
A table saw with a decent blade can cut wood to a very smooth feel.
If you are not able to cut to the desired smoothness, then you may end up needing to apply some product to fill in the roughness of the wood.
Take a look at SlipIt. One of several options.
http://www.woodcraft.com/product/2004247/9013/slipit-jell-1-pint.aspx