Great question, but no, the X-15 was not a "critical and necessary step on the path to manned space flight" at all, it was used to test the feasibility of sustained and controlled
hypersonic flight of an aircraft at very high altitudes and speeds. The X-15 was an extension of the X program, started in the 1940s, to continuously push the speed envelope of aircraft through the sound "barrier", and the thermal "barrier" beyond it.
Manned space flight, requiring rockets with much more thrust for far longer, simply is in another league, and was founded in the ICBM programs of both the US and USSR, which owed much of its foundation to the pioneering work of Goddard, and the development and scale up (including the all important turbo pump) of team von Braun.
Recovery systems from these flights were, and are, capsules. It is rather dumb to haul an airplane into space when payload to orbit costs are measured in thousands of $ per pound.
The Space Shuttle was an awesome technology demonstrator, but never succeeded as a low cost replacement for ordinary rockets to move cargo to orbit, but remains a viable option as a means to return cargo and crew from orbit.
So, although the X-15 did reach the edge of space on some of its flights, and did use control thrusters, it was much more an airplane, and should be more than welcome as a subject for readers to enjoy on Aviation Stack Exchange.