The truck is indeed moving up the hill, and the tires are not slipping. There are a couple of ways to see why the friction points in the direction of the motion of the truck. One way is to keep in mind some external agent must be acting on the truck to get it moving to the right. That is, in your free body diagram there has to be some force acting to the right to get the truck accelerating to the right. You might say that the engine and tires are the thing(s) doing this, but keep in mind, if the road was perfectly frictionless, then the truck would just sit there with its tires spinning. As we turn on friction slowly, the truck wouldn't all the sudden start moving backwards, it would start moving forwards. There is a force responsible for this, and its friction.
Another way is to circumnavigate the above all together and note that the truck is pushing on the road down and to the left, hence by Newton's third law, the road must be pushing on the truck up and to the right. The force that points upward on the truck is the normal force, and the force that points to the right is the (static!) friction force.
As per your comment you still seem confused, thats fine. In which case, forget the truck for the moment and let me build up the logic more orderly:
(1) First of all, we have to agree how static friction works. Picture a block on a table with a string attached to the middle of it, and you pull that string to the right. Friction is what opposes the motion of a block sliding on the table, and it always points opposite the motion of the block. If the block is sliding its kinetic friction thats opposing it. If the block isn't sliding, its static friction. Static friction opposes whatever motion the pull intends for the object. For example, if you are pulling the block to the right on a friction-full table, and its not moving, the static friction is what points the left that opposes the motion. Its critical that we agree that this is what static friction is, and how it works.
(2) Now replace the block with a wheel so it can rotate where the string it attached to it (that is, it can roll if it wants to). If the table is (perfectly) frictionless, and you pull on the string to the right, the wheel will just slide as the block did.
(3) Now lets say we turn on friction. The very bottom of the wheel wants to go to the right, but it won't - it will stick (i.e. won't slip) because of friction and the wheel will roll. Remember from the block example above friction is the force on a surface that will oppose the motion of the object if there was no friction. The bottom of the wheel wants to slide to the right, so (static!) friction opposes this and points to the left.
If you still have further questions feel free to let me know, but let me know if you disagree with (1), (2), or (3).