Sailboats can already go downwind faster than wind by sailing at an angle, no additional equipment required.
No additional equipment required, unless you want to sail directly upwind
You can sail upwind all the same, albeit not literally straight, but by sailing zig-zag.
I understand that. It is called "tacking" right?. My question is could a rotor + propeller allow a sailboat move upwind faster than without them, and possibly even move directly against the wind.
Based on the article it seems plausible to me that it could move faster. But would that be against the rules of some major sailing competitions?
Blackbird works because of the friction between the wheels and the ground. On the water you don't have that, so I don't expect it to work.
You could have friction between a propeller at the end of the boat and water.