The 68000 does nothing; it is entirely disabled. Ditto the Yamaha OPN.
The Mega Drive's VDP is almost entirely backwards compatible with that of the Master System — it implements the graphics mode used by all but one of the Master System's games natively*. So there's no emulation or translation, it's just a different graphics mode.
Similarly the SN76489 is exactly the sound chip used in the Master System, so it's just presented as is. With a potential caveat: the physical chip might be absent; Sega rolled a reimplementation** into the VDP for the Master System 2 and Game Gear so I dare imagine its functionality got subsumed in the Mega Drive too.
In short: the relevant components are hardware-compatible with those in the Master System [almost] as far as it matters; the others are disabled when a Master System cartridge is detected.
If you wanted to produce your own at-home alternative to the official adaptor for Master System games all you'd need to do is:
- ground the Mega Drive's M3 cartridge slot pin, to signal that the Mega Drive should run in Master System mode;
- connect all Master System cartridge port pins one-to-one with the Mega Drive equivalents; and
- add a physical button to trigger NMI, that being what the Master System's 'pause' button does.
* The Master System is in-turn backwards compatible with the SG1000, reimplementing its graphics modes (which as those of the TMS9918a, also seen in the ColecoVision, MSX, TI-99/4a and others). The Mega Drive omits those. One early Master System title, F-16 Fighting Falcon, uses one of those modes rather than the Master System's native mode.
** Sega's version has slightly different noise-channel output, as it uses a different LFSR polynomial. But it's similar and the exact noise waveform isn't that important to Master System software.