that is strange, i checked your video, and now every 3rd time when i jump back and forth the block on right side and i go to jump on the left where initially the player was, the up press key doesn't work, well it detects the key input but doesn't jump, there is a bug somewhere, to me that looks like a logic delay for some reason, cause if u do it slowly it never fails, but if u do it fast really fast like super-slight-tap like that's when happens on my side atleast.
you glitched me as well lmao ... but ... if the gameplay you are after, isn't very fast paced, considering the fact it works if u don't go bananas fast on the keyboard id say is one of those things u gotta accept? :D
Edited: the glitch happens no matter if u are near edge or not, or your falling, is just a delay logic somewhere(not in the templates event coding, cause its a very basic no delay action type of thing), and the condition considers already jumped for some reason even though visually u landed, the system still considers your 2 frames still falling(this is commonly referred as "jerking" where you visually see stuff that should been happened but actually the render is way ahead of the what actually happens).
this might be a platform behavior glitch or logic function, id file this as a C2 bug, but it might take a while for C2 to be updated, now is a matter of testing it on C3. il be back with that.
Edited: still happens on C3 also, but on C3 happens different, isn't about how fast u tap, but more of where you land... like you said, near the edge... so if you land near the edge of the platform, the player is considered still in the air, this might be the 2 px glitch i always seen on the animation editor in C2, it has to have something with that... that glitch basically when u crop the empty space before the latest version the animation editor would've cropped it up to the very edge of the color pixel but now it ads a 2 pixels margin around the character... and this probably cause of that... on C3 that doesn't happen on the animation editor anymore, but it seems the logic of it is somewhere in the behaviors also not only the editor itself. id file it as a bug on C3 as well, cause C2 we don't know when is going to be updated, or if there is time to focus on C3 and C2 ... till then as i said above, is one of the things you have to live with if you using that platform behavior, or just find another workaround it (like manually create the collision and character movement in the event sheet, is tedious i know... but will be more fail safe.)