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The Sega Genesis / Mega Drive's main CPU, the Motorola 68000, was a 32-bit processor. Couldn't Sega have marketed the console as a 32-bit device? Or is there a technical distinction about how the 68000 was used in the Genesis that makes the system, as a whole, 16-bit?

My best guesses are that it has something to do with word size (the 68000 can address bytes, 16-bit words, or 32-bit long words) or the size of the buses inside the console. Still, I would think that Sega's marketing team would've chosen the most beneficial number when looking at the technical specs.

... the Motorola 68000, was a 32-bit processor.

As already written, Motorola itself said that it is a 16-bit processor.

And as far as I know, the reason is not the external 16-bit bus but the inner architecture of the 68000:

The 68000 only had a 16-bit ALU, which means that it could only perform 16-bit operations.

The CPU executed 32-bit instructions (like add.l) by performing two 16-bit operations internally.

This 16-bit ALU is a major difference to CPUs like the 386SX that also only had an external 16-bit data bus but a real 32-bit ALU - and therefore were called 32-bit processors by the manufacturers.

It's usually the width of the system data bus that determines the "bitted-ness" used to describe the system.

While the Motorola 68k CPU used as a component in the Sega system certainly has some internal 32-bit capabilities, most notably the width of the register page, and is designed for upward compatibility with full 32-bit CPUs (like the 68020), the reality is that the 68000 only possesses a 16-bit data bus. Likewise, the Genesis system data bus is also 16 bits.

Also, at the time of the introduction of the Genesis, it was very competitive with the technology in other game consoles. So, there was no need for Sega to try to bend the truth with some over-zealous marketing scheme attempting to brand their new console as 32-bit capable. Instead, and only later, did they get into a bit of technical hyperbole with their marketing of "Blast Processing" aimed at the SNES.

the Motorola 68000, was a 32-bit processor.

I'd say 16 Bit - likewise Motorola did (*1).

The bitness of a processor is and always will be up for discussion, as various features may not operate at the same size. An 8088 can be (an has been) called an 8-bit CPU as well as 16-bit. Similar the 68000 with its 32-bit registers but 16-bit bus. Beside data bus and register size, the ALU can as well be used (*2). Last but not least operand size may be a valid criteria (*3).

Couldn't Sega have marketed the console as a 32-bit device?

Yes, the could - but there would have been no gain. At the time the Genesis was introduced (1988) there was no race for 'more bits' especially not in the general public. The prior generation wasn't marketed as 8-bit systems. That's a label that got only retroactive assigned when 16 Bit systems became popular and marketed as such.

It was about setting a undoubtedly new mark, making everything else look outdated. The second half of the 1980s was also the time when bitness was used to distinguish the 'new' and 'better' computers with the very same label. Atari ST, Commodore Amiga, as well as 286 PCs, where marketed as 16 Bit machines, so the label was already promoted and present in non-geek-minds (*4) as a sign for being the better choice. Hooking up to an established label is almost always better than trying to build a brand from scratch with all new attributes.

Bottom line: Calling it 16-bit (which it undeniable is) was the best bet for Sega marketing.

Sidnote: Atari's attempt to sell the Jaguar in 1994 as 64-bit console might as well have worked less than expected for the same reason: Consumers just got used to consoled being called 16-bit and having 32-bit coming up. Jumping too far ahead doesn't work well.

*1 - The same way next to all manufacturers of 68000 machines did call their products 16-bit computers - or 16/32 as most.

*2 - Making the Z80 a 4-bit CPU :))

*3 - Thus the (16-bBit) Z8000 could be rightfully called a 64-bit CPU :))

*4 - Like always, dad has to pay for a new console and he needs as well a reason to crank out more paper slices than for some other game console - having Sonic didn't ring a bell.