Letter of recommendation before Skype interview
If the 2-3 weeks are after the deadline, it looks like they are shortlisting. If the 2-3 weeks are immediately after the deadline or before the deadline, one can't rule out the possibility that they haven't shortlisted and that they just remind of incomplete applications.

On another note, I wouldn't take reference letters too seriously, nor would being asked for reference letters make me excited. Letters from prestigious persons don't help too much unless several candidates are tied, in my opinion.