moving all sorts of objects and people around with the power of their mind
What other power could they use? Their physical form doesn't seem to have mass or substance to speak of; every time they move an object, they are really using a power alien to us.
I think someone as imaginative as yourself could come up with several other explanations for Laas's ability to do what he did without Telekinesis. Perhaps he just shapeshifted into a solar sail for most of his journey and that allowed him to pick up speed more and more in the inertia of space.
Laas is not a limited creature. He can turn into fog or fire; suggesting that he can't propel himself through space on the power of his mind is inconsistent and unnecessary.
Unless we categorically assume that Laas doesn't actually shapeshift and act, but merely creates the illusion of that in the minds of the observers. It may be that this is how Changelings work. But then again, it would also be a good explanation to how Armus works: like a Talosian (only better), he tells our heroes to throw their phasers into the tar pit, then tells Riker to dive in there, too, and in reality he's just a small, balding man behind the curtain and nothing he appears to do actually takes place physically...
Really, it's pretty hopeless to disprove that a creature of great powers would not be related to another creature of great powers: the powers themselves automatically enable the connection in all circumstances. The only "proof" comes from the dramatic undesirability of a connection: in a galaxy full of wonders, why should any wonder A be related to B? Well, if the story connecting them is good, why not?
Timo Saloniemi