Yes, Kylo coming into his own is Kylo putting the past behind him. His father is just one part of that, his grandfather is the other. At the end of TFA (and the beginning of TLJ) he is conflicted. As Snoke points out, killing his father didn’t resolve him.
Considering how there was much speculation that he’d become Vader v2 in this, this scene is incredibly important to establish that he’s forging his own path.