Upvoted without even watching the video. This is important to know. I just hope you realize that every support has 2 styles, a primary and a secondary. For instance Taric is a sustain/kill support. Q gives him healing and W gives damage mitigation which plays into the sustain methodology. E W and R grant him kill power what with his point and click stun, his armor shred and his all-around steroid booster ultimate. Taric's only form of "poke" is his stun which does less damage at longer ranges. So Taric is an upclose and personal fighter who has a functional amount of sustain. He still needs buffs though.
Sona, the main champion in the beginning of your video is a poke/sustain laner. She excels at poking with her Q + passive burst damage. Even though she is a support she can out trade anyone with the sheer amount of damage in her combo. And if the enemy pokes back she can heal it all back with her W. E is best used as a peel ability. Speed up herself and her allies and then auto and peel away the pursuer with an auto attack. Her ultimate is an AOE stun which again works best at peeling or followed up with burst damage. Despite her raw power Sona is not a kill laner because she is horrendous at DPS output. Once her Q and R are on cooldown she only has her auto attacks to kill someone which is extremely unreliable. And she sucks against anything with a gap closer.
Nami is a poke/sustain champion. Soraka is actually a better example of sustain. Or Janna. Or Bard. Sustain is their primary style. Bard, Soraka and Janna are sustain/poke laners. And Alistar and Taric are your sustain/kill laners.
Leona is indeed the best example of a kill laner. Leona's secondary style is poke thanks to her passive. Other kill laners are Blitzcrank, Thresh, Annie, Zyra and Nautilus.