The problem is that when Plank tries to open Clementine (from the Plank icon), it uses the Clementine default behavior.
Since Plank is trying to open Clementine for the first time, it will use the default preference, which is: "When Clementine starts" - > "Remember from last time". However, opening the first time in Plank, there is no "last time", so the GUI does NOT open. Here it is in pictures:
Simply change the default behavior of "when Clementine starts" to: "Always show the main window":
Done!
The "Proof":
