Transputers were novel in that they combined a CPU core with a set of high-speed network links: the CPU ran at, eg. 20MHz and the four network links at 20Mbps.
Paired with this hardware was the programming language Occam, which was derived from the ideas of Tony Hoare's CSP, and included concurrency and communications primitives that mapped directly onto the Transputer hardware.
The end result was a system in which it was easy to configure a parallel machine with a mesh, torus, or tree of CPUs that could then run CSP-style concurrent programs very effectively.
While it saw some success in various niches (image and signal processing, for instance), the Transputer CPUs did not support other popular languages of the time (C, Pascal, Fortran, etc) well, and for various reasons, Inmos was unable to evolve the design to match the performance of (in particular) the Intel x86 family. From an initial position of having competitive performance and superior concurrency and communication, the Transputer was quickly left behind, and its successor (the T9000-series) was obsolete before launch.
I think the failure to keep the single-CPU performance edge was probably mostly about lack of money vs the competitors. Obviously related to not selling enough of the first generation chips.
The article also discusses the reasons for the lack of follow-on investment.
There was -- used for scientific computing on things like the Meiko Computing Surface, though not by me.
Exotic parallel architectures: you can build it, but will they come? Usually, no. You need some widely used case that partitions to match the hardware. GPUs and Bitcoin mining are the big successes so far. Machine learning has that property. Successes in this area tend to come from needing to solve a specific problem at scale.