The overall wave is traveling to the right. The individual particles in a transverse wave do not move to the right. They move up and down. What you see as a "wave" is really just the procession of particles moving up and down in sequence. They are moving in a direction transverse to the direction of the wave!
You can simulate the effect with a bedsheet that's tucked in on both sides. Place a small object on the sheet and then slide your hand underneath it. You can consider the direction you slide your hand to be the wave's direction. You'll notice as your hand approaches it, the particle itself doesn't move in the same direction as your hand, it moves up. As your hand passes underneath it, the particle begins moving back down (this is where the particle in your diagram is).
If the wave were a longitudinal wave (a compression wave like sound waves and waves down a slinky when you give it a push along the length of the spring) then the individual particles would move parallel with the wave direction (the individual particles still stay close to their original position, only the wave travels).
In fact, whether a particle moves perpendicularly or parallel to the wave's direction is what defines whether a wave is transverse or longitudinal.