It's pretty obvious to me that those that are flabbergasted by the concept of a 1st round pick for a (retained) Dowd haven't watched much Capitals hockey recently. I don't blame them, the Capitals are playing some pretty boring hockey. Not a fun team to watch on a nightly basis.
But Dowd has been one of the bright spots on an otherwise dim team. He faces absolutely brutal deployments (he starts 8 shifts in the defensive zone for every 1 shift he gets to start in the offensive zone) against the opponent's top line forwards. He's an excellent shutdown center, who does a surprisingly good job chipping in offense given his role on the team and the match-ups he faces. Calling him "4C" is also underselling his role on the team as a whole, given that he has more ice time than per game than Connor McMichael (and only 4 seconds less of ESTOI/GP), and with the decline and subsequent LTIRment of Backstrom, the Caps can't really afford to try their other centers in the shutdown role to free Dowd of this duty to give him more offensive situations.
Equally important is the fact that Dowd isn't a rental. He still has one year remaining on a his very reasonable $1.3M deal after this season. And, in the situation described in the OP, if the Capitals would really retain 50% on the deal, the acquiring team would have their shutdown center locked up at only $650K against the cap (which is beneath the league minimum) next season. So that type of contract value is pretty damn hard to match.
Why do the Capitals move him? Because this team isn't going anywhere fast, and Dowd is 33. By the time they're ready to compete again, he will be on a new contract and likely declining. So sell him at a high point in his value, utilizing the cap situation to their advantage to maximize the return.