Really unintuitive, I thought that only the speed in the same direction would be influenced!

Time is (equally) changed for all directions, so the speeds must have changed too.

OK, I get it that the co-ordinates of the moving 'object' were taken from the perspective of the stationary 'platform'. And that when these are translated to the perspective of a frame of reference moving at velocity V in the x direction the spatial co-ordinates of the y and z components remain unaffected but the time component will be, and as Velocity = Distance/Time then the Velocity must therefore be affected. So far, so good - but much more of this and my brain will boil!

Roger the brain boil🤯... Roger Roger, Vector Victor 😉