They likely mean { X, Y, Z, T } three spatial dimensions and time which are four orthogonal dimensions.
That said, it makes the "moving in" redundant and is shy a few dimensions if you want to go full descriptive phase space diagraming given velocity and acceleration in each spatial dimension are missing.
I suggest you take your objections up with the authors of, say,
A Four-Dimensional Space-Time Automatic Obstacle Avoidance Trajectory Planning Method for Multi-UAV Cooperative Formation Flight
or any number of other similar papers.
Many prefer to think of an objects path as a trajectory in space-time (four dmensions) and for two ojects to "collide" their paths must coincide within that 4-D space within an Epsilon for some value of WTF.
But as ... you yourself ... note above, the planes aren't moving in four dimensions. If time is one of the dimensions, all the planes are doing is existing.
The path of the plane is a static curve in 4-dimensional space, yes.
But the plane is not located at any point in the 4-dimensional space, and the position in 4-dimensional space that it doesn't have is not changing over time. Both of those things are required before you can describe the plane as "moving" within the space.
There is no secret backup time that will allow you to track the plane's hypothetical motion along an explicit time dimension. That's not a thing.
That said, it makes the "moving in" redundant and is shy a few dimensions if you want to go full descriptive phase space diagraming given velocity and acceleration in each spatial dimension are missing.