I fast-forwarded the video and didn’t find the part that mentions how the weapon is implemented. Perhaps it only talked about how to switch between weapons instead of how to implement a weapon system.
As you may have already done, you would need to first create the base class Weapon with variables FireRate and MaxAmmo, then create two subclasses Rifle and Shotgun both inheriting from Weapon class. I assume you are using blueprint, in which case you need to initialize FireRate and MaxAmmo to the desired values in the BeginPlay() method of the two subclasses.
Let me know if this solves your problm.