Extra Wire in Light Switch Box?
You have the right idea

You understand that a wire going into a backstab right next to the screw is the same as going to the screw.   And you understand that when a wire goes to the backstab, and another goes to the screw right next to it, those wires are also connected to each other.  

Let's pause, to remove confusion, and take that load/switched wire that was on the old right switch (the black one) and mark it with let's say yellow tape because it'll match that Lutron.

Respect how it was before

Now, look at the previous configuration.  You had the supply wire, a switch's lower screw, the pigtail between switches, the other switch, and this mystery wire all connected to each other.  And they are all black.  And they are the only black wires in the box (since we re-colored that yellow).  And, spoiler-alert, they were all intended to be always-hot or "line". 

Since they're meant to be together and are the same thing...  Connect them all together.  So you'd join the 2 black wires from the wall (i.e. not yellow) with the 2 black wires or pigtails to the new switches.