I'm going to try and add to the discussion.
1) I initially mis-understood gouessej's comment as "switch to GL-ES" or do that part in GL-ES. What he probably actually means is you can use GL2ES1 "constants" as parameters in GL3/4 glEnable calls, e.g.
GL3 gl = drawable.getGL().getGL3();
gl.glEnable(GL2ES1.GL_POINT_SPRITE);
which solves the problem for me, although I am not sure how legal or illegal this is.
2) I do not have this problem under Mac OS. It only manifested itself once I tried the code on Windows. I assume that is a driver difference thing (?), not a problem in JOGL.