In our syllabus this is sumi otoshi
: tori goes down on his knees and blocks knee or foot of uke.
The version shown in this thread as tai otoshi is called kokyu nag at us.
That's a nice vid btw...
Though in our school we call this aikiotoshi but I really can't tell you why.
As for tai otoshi, typically we would call that from an ushiro Ryotedori/tekubitori kokyunage throw to the front.
But i'm the last person to argue about semantics or names so when in Rome...