Is it sitting on a treadle cabinet top, in the first picture? Even if it isn't a treadle machine it will still need a smaller belt that will attach from the hand wheel to the motor. You can see the thing that is sticking out the side of the motor in the 2nd picture. When you step on the foot control to run the motor, then the thing sticking out (with the belt around it) will spin and this will make the belt turn the hand wheel which will then make your needle go up and down. I hope this is clearer than mud!
I'm not sure why the dealer said that you don't need a belt because you do need a belt. Do you have more pictures from a little further away so that we can see the whole machine?