But Spectre cannot break kernel memory. Its more of a "new class" of bug, similar to how "Buffer Overflows" don't describe a particular attack, but a methodology that hackers will use to exploit new bugs.
Spectre affects virtually every high-performance computer in the world. Smartphones, SPARC, PowerPC, Intel, AMD, ARM. All of these designs use out-of-order execution, and in theory, a rogue Javascript would be able to read the rest of process memory if a programmer isn't careful about how things work.
Meltdown took it one step further: and showed that code could read Kernel memory. That was an Intel-specific mistake.