Very good question. AFAIK there is no single, agreed-upon definition.
So, is Guild Wars a MMO? or D&D Online? Both of those are basically trading hubs from where players enter instanced adventure zones in small groups.
Is Star Trek Online a MMO? Most of the content is instanced and only available to solo players and small groups.
Is UO a MMO? Was it a MMO at launch, despite the lack of guilds, the restrictions on chat, the lack of proper group content?
Is Simcity a MMO? After all, players play together in zones, and trade across a global market that reacts to each transaction.
Is WoW a MMO? For many players, 90%+ of the time is spent on the personal (instanced) garrison, from where the player only emerges to teleport to the (instanced) dungeons and raids.
Does the addition of different ways of doing things, ways that bypass much of the player interaction, changes whether a game is a MMO or not? For example, when WoW and Rift (and about every WoW clone) added ways to simply click on a button and be added to a dungeon or raid group, did they become any less MMOs?
What about Second Life? Are game systems even required for a MMO?
The MMO genre is so diverse that, sincerely, expecting the features of a specific MMO to be available across the whole genre is like expecting Zelda to have random loot and gear grind just because it's an action RPG.