The real world also can have thousands of dimensions. Time, color, hatred tension in the room, air current, and anything you can possible attribute to a position/thing.

At the end of the day it's just words, and their meaning depends on agreements. When we speak of the 3 dimensions, we mean the 3 dimensions of the physical world that we decided to define with 3 coordinates that help us known the position of something. Might as well have used complex numbers and keep it to 2 coordinates, or decided time should be included as part of the concept of position. So when you talk about "dimensions" in general, it may as well mean anything.