Uber really only has two things in common with public transit: cars and buses both have wheels to go places, and the services are both paid.
{1} On-demand vs. scheduled
{2} The given number of cars in the field sets a harder upper limit on number of riders. With buses, it's basically always "pack more people onto the bus, no matter how crowded" (i.e. the bus is forced to approach closer to "theoretical" carrying capacity of vehicle's physical volume - compare this to how much Uber is used for single riders.)
{3} Anti-"troll" filtering (I mentioned elsewhere that this works for the same reason it works on web forums - you eliminate the irresponsible elements.)
{4} No routes with Uber: go where you want. Normally this flexibility costs you at the rate of a taxi.
That's not a full pictures of their current offerings. UberPool/Lyft lines are already closer to public transit on the continuum, with respect to the distinctions you made:
1: Pool/Lines add a lag to search for a match, so it's a bit less on-demand and more favorable others' schedules.
2: Pool/Lines increase the riders/vehicle.
4: Lyft Line hotspots reward you for picking start points at special locations, and ending within a zone, so it's somewhat route-constrained in return for a lower price.
The article's prediction (and Uber's upcoming initiatives) simply go further in that direction: more constrained routes, more constrained times, lower prices. It's not the sharp boundary you suggest.
{1} On-demand vs. scheduled
{2} The given number of cars in the field sets a harder upper limit on number of riders. With buses, it's basically always "pack more people onto the bus, no matter how crowded" (i.e. the bus is forced to approach closer to "theoretical" carrying capacity of vehicle's physical volume - compare this to how much Uber is used for single riders.)
{3} Anti-"troll" filtering (I mentioned elsewhere that this works for the same reason it works on web forums - you eliminate the irresponsible elements.)
{4} No routes with Uber: go where you want. Normally this flexibility costs you at the rate of a taxi.
Etc.