The spiritual successor to the transputer is a company called XMOS[1], which has some of the same original people behind the transputer there. You now tend to have multiple cores (virtual and physical, each virtual core is handled by time-slicing in hardware, and physical cores are other instances of the same) on a single chip-carrier, more memory, and embedded hard-cores for ethernet/USB but the concepts are pretty…
Modern multi-core computers all use an interconnect/network-on-a-chip to communicate across cores. Shared memory multiprocessing is built on top of that networked architecture, using cache coherence protocols. They also commonly use SMT which gives you the "virtual/logical cores", better known as hardware threads (harts).
These are nothing at all like the links that Transputers use to communicate internally.