Internal energy is also called thermal energy, so the mark scheme puts thermal there in brackets as an alternative name. Internal energy is equivalent to the sum of the kinetic and all potential energies.
You may be aware that temperature is defined as the average kinetic energy of the molecules in a sample, if this helps wrap your head around why "thermal" and internal can be synonymous. Or, things that move faster are hotter, in simpler terms.
And yes, due to friction, it is transferred to the thermal energy store of the box and the ground. This actually flows as heat here, meaning that the temperature here increases (which, if you think about logically, does make sense by observation. Friction makes things hotter). And by our earlier definition, that means kinetic energy has increased.
So the kinetic energy of the particles of the box in one part has actually increased, but heat's definition includes the transfer of energy, so energy is being transferred to the ground as well, and vice versa.
So overall, if we were to take the box as a whole, as both mass and speed are constant, its kinetic energy is constant. However if we were to take the particles at the part of the box in contact with the ground, the temperature (and therefore average kinetic energy) here is changing.
Due to friction and it being a level surface, the work done is not being stored as potential energy. It's wrong (I think? or at least, misleading) to say that the kinetic energy of the box is changing due to the above reasons, but the potential energy is not changing either. So technically saying that the internal energy of the box has changed would also be wrong (as it is the sum of the other two).
Rather, the energy is stored as thermal/internal energy in the box as well as the floor, which is why both are specified in the answer.