Historical reasons. Initially was inspired by TeX and Emacs. The project started in 1998 so now is hard to change the name. For the moment there is no consensus on a better name, so we stick with it and just try to make it clear from the outset.

I never used LyX so I cannot compare. The point I wanted to make is that in TeXmacs cursor movements are actually movements inside the document tree and there is a notion of current focus which is the innermost environment you are in. Many operations involve the current focus (e.g. you can switch from a Theorem to a Lemma or change round to square brackets with one keystroke). Then another peculiarity of TeXmacs is that what is on the screen is exactly what will be on the PDF, because the same typesetter is used for screen and PDF output.