I don't know what any of this means but to me it was just "oh look, he's not dead yet", I thought it was lame and he didn't even seem like a very fun boss fight anyway.
The changing moveset in the first phase is meant to signify Soul of Cinder is an amalgamation or avatar of all those who lit the flame (the player characters) in previous games and then the second phase is the first one who lit the flame - Gwyn, bringing it full circle.
Thematically, I think that is a really awesome ending to the series, but as a fight from a purely gameplay POV,I was very underwhelmed by it - these 1-v-1 duels just aren't my thing. I like the wacky fights and big monsters personally, but I get that's not what a final boss is going to be, so I think Soul of Cinder was satisfactory - its design could've been better though, something more haunting or ethereal maybe. It just looks like a random undead king dude, and they still had a boner for the flower field thing from Gerhman in BB, so we got that again.