The diagram you posted is incomplete. Although the drive roller does have a force acting on it that pushes it towards the front, it pushes equally briskly on the tire in the other direction. Essentially all the non-rotational forces on the bike, generated directly by the roller, balance out. (They are transferred to the seat stay and then through the chain stay to the rear axle. Essentially, the bike frame acts as a rigid object, and all forces acting internally on the frame/axle balance out)
You could also think of the tire as a lever, and the axle, as the fulcrum. The drive roller pushes forward on the top of the tire, it rotates, and pushes rearward against the road surface. The motor PULLS against the seat tube/seat stay, and they in turn push against the seat stay and chain stays, eventually pushing against the axle (the fulcrum.) Since, under normal operational procedure, none of the individual pieces of the bike fly away as you're using them, you can be sure that the net force on each piece sums up to zero. (for every positive acting force, there is a negative acting force to balance it.)
However, the torque is converted to a net linear force 'where the rubber meets the road.'
The Wheel is an idler roller, and IT is what is pushing the bike forward. Granted, the motive torque comes from the engine, via the drive roller.
The forces on the rubber of the tire cause it to deflect (as a type of spring, if you will) and act on the rest o the tire, less any small internal frictional losses due to the distortion of the rubber surface.
There are also generally one or two drop rods, used to apply the tension to the drive roller, keeping it against the tire. The two triangles formed by the bike/drive system as a whole (ref the attached pic) keep the assembly rigid, and transfer the forces so that no net linear force is generated anywhere, except at the tire-road surface interface. Think about it - if there was a NET linear vector being generated at the motor, it would fly off. All the linear forces everywhere on the bike, they all balance out. except at the road.
And, if the net linear force weren't being applied at the rear tire/road interface, if the bike were sitting on a perfect frictionless surface (super ice) , it would move forward when you goose it. But, on a perfect frictionless surface, that wouldn't happen - the rear wheel would spin, and you would sit there blowing smoke out the exhaust...