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It was about setting a undoubtedly new mark, making everything else look outdated.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.