That appears to be intention, there was no weapon in models he provided, nor animation to support firing it. projectile fires from midpoint between arms. I assumed that for brevity, he made decision not to go further. Once you get into adding a weapon, you could to detach and attach other weapons and build a class to support that, keystrokes to pick up and drop, etc. Then projectile would logically have to be a child of that class. It could go on forever with FPS possibilities. tutorial would get quite a bit longer and become more difficult for a new person. In my opinion, it was quite instructive by stopping where he did, and a good length.
If you want to create your own, find a weapon model, import it, and scale it to his models. Then create a class much like you did for FPSProjectile and extend a blueprint from that like you did for BP_FPSProjectile. Spawn that as a child of FPSCharacter. You can spawn it in constructor of FPSCharacter, just like you spawned Character in FPSGameMode. Position it using SpawnLocation that he shows how to use in FPSCharacter. That should give you a weapon that follows your arms moving as they “breathe”. Then change muzzleoffset defined at spawn of FPSProjectile (found in “Fire” section of FPSCharacter) to be at end of your barrel so that projectile appears to come out of your weapon. Some nice touches would be to decrease scale of projectile (sphere) and alter two physics parameters in BP_FPSProjectile (Play with values for Initial Speed and Max Speed in Projectile section of ProjectileMovement component of BP_FPSProjectile) which will make a faster “bullet”. I believe tutorial contains all samples of code necessary to do these things.