kotl is really strong this patch because he can mess up the enemy carries very easily from the very beginning of the game and i've been playing him a lot myself, so good choise there.
i think there are some really big question marks in this game tho:
1) get a value point in mana leak before level 4, it's mandatory (1-1-2 is good at level 4). use it on the enemy that needs mana the most and then right click/horse him: your laning phase was really weak, while kotl is supposed to make the laning phase a nightmare.
2) i'm watching the game in player perspective, and you always have your eyes on your hero, which is totally fine if your first priority is survival, but this is not the case. as soon as you see a fight, keep your eyes on it, ulti, start channeling, mana leak the most appropriate target, use blinding light when they start right clicking and (even more important) to mess up positioning and escapes. when you play kotl you MUST do 100 things at once, not just spam horses from behind the trees: if you don't used all your spells as kotl (and you don't have mana problems) you're not doing it right.
3)starting items: i start with courier, wards, 1 tango and ring of protection, so i can make tranquils at the side shop as fast as possible, and as you can see you had problems with the courier.
4)don't rush scepter like that, get force staff first (and then urn, mek, pipe, necro, whatever is useful for your team: having vision is fine, but if you can't heal and save your team you're just seeing better how they're gonna kill them all), it's absolute core: you have no idea of the plays you can do with kotl and force staff (including escape, force staff a manaleaking enemy, force staff yourself and blind people exactly where you want, chase and mana leak a fleeing enemy, SAVE an ally after pushing back the enemies with blinding light)
5)whenever you see an enemy (42:30 for example), mana leak him so he can't just run away, then you can start doing your kotl things.
6)your positioning as kotl should be just outside the fight with your eyes on it, in range to use spells and items, and i've noticed you're always too far away, sometimes even too far away to spam the horses.
hope it helps.