Thus does not really work for chemical fuels. They are literally turning their fuel into other things! So the recycling portal is not picking up more fuel, it is picking up exhaust. Exhaust which it cannot extract more energy from using the same chemical process.
If the "fuel" is for an ion drive, this scheme has some merit. This is because the thing which gets thrown out the back is the same thing which it needs to accelerate. (The "reaction mass," to use a formal term.) So you can use electric fields to accelerate the ship using the same ions over and over again. The ions get progressively faster, as does your ship, without needing more ions to lug around. It should be noted that this still requires energy to accelerate, so really some electricity is the actual fuel and the "fuel" in the diagram is a reaction mass (the ions).
This is unclear with these portals. Do the portals conserve momentum with the particles entering them? If mass and acceleration are the same for the particles going in/out, then the math technically works, because linear momentum is a function of mass and velocity, not position. Usually, an abrupt change in position means a change in momentum, but hand-wavey portals are now in play.
Conservation of energy may be the issue: several forms of energy conservation are position based. I suppose that is the cost of these portals.
There is also the issue of maintaining a portal in front and behind the craft. The portals need to move with the craft, otherwise it loops around infinitely. I suppose that could still be useful: accelerate in place to some appreciable fraction of the speed of light, and be really careful about when you turn the portals off and zoom into space.