It's more nuanced than that; the approach you're describing is usually called "decompilation."
The difference is how far one goes in hoisting the "source code;" in this "recompliation" approach the source code, while C++, is basically an IR (intermediate representation) between the original game's assembly and a host platform, and the hardware itself is emulated (for example, the original architecture's CPU registers are represented as variables in the host architecture's memory). The machine code is translated to C++ using a custom tool.
In a "decompilation" approach the game logic is converted (using a decompiler, like IDA or Ghidra's) back into something which resembles the original source code to the game itself, and the source code is usually hand analyzed, marked up, rewritten, and then ported across platforms. The product is something that attempts to resemble the original game's source code.
Of course, they lie on a continuum and both approaches can be mixed, but, while they both involve C++ in the middle, the process is starkly different. Recompilation is much more copyright-friendly, because in many implementations only the modifications are distributed and the original binary is translated by the end user (who owns the software/a license to it), whereas decompilation produces an artifact (source code) which is a derivative work encumbered by the original software's license and generally should not be distributed.
