I think it is MMO enough to qualify. When people read it has a Multiplayer mode, next to a Friends Only online mode, Solo online mode and a Solo offline mode, they think that at most this will be some sort of "hub" game. MMO= thousands of player in the same world. However MMO's have been segregating players since UO, in servers, instances and zone-copies. So is it a question of, how many players are in the same, *continous* space? When you go to Everquest, you are either with 100+ people in a tight spot (like any hub-zone where players gather such as the PLane of Knowledge) or you are very likely to be playing with 1- 12 players in an XP-zone, maybe. Still a MMO.
Shroud of the Avatar (multiplayer mode) will have cities and towns, with persistant housing, which will act as hubs with hundreds of players simultaneously. So the house that you put up in let us say in Akalabeth Village will be visable for everyone that is in that village. Now if the town gets overcrowded, a new instance of that town will be created, *with* your house. There will not be different servers. So though the owner (player) of the house may be in Akalabeth instance 1, you may be in instance 2 and thus can not see him: but you do see his house. I think this is still better then putting people on different shards. Your house is persistant through all instances,and your character can hook up with anyone playing SotA. This is more Multiplayer then many MMO's out there.
Now for the continous world: from these towns and cities you will walk up to the edge then go into an Overland Map: there is still some debate how this should look. It was initially stated that this would be a very nice 3d exploratory kind of map, top-down view like in Age of Wonders or the Civ games. Anyway, you roam this Overland Map untill you reach a spot where you can enter a "scene": this can be anything, from a dungeon, to a stretch of Forest to a Hamlet full of bandits. In this scene you return into normal 3D MMO-mode and can then explore this scene.
How will these scenes be populated? I am unsure as of the amount of players that can populate such a scene but I have heard a few dozen at least. The players that are in your scene are also differentiated by toggles you can set ( I think), by your party members, by Guildmembers, PvP or not, or according to language(settings): so basically some sort of "smart-matching". The good thing about scenes is that they can be easily tailored for cool Quests, can show progression and change in Stories, and new scenes can basically be implemented infinitely in the overland map, since there is no continous world in the old sense.
So if you want to walk out of the gate of your town, and want to keep walking without interuption, till the end of the world, encountering players here and there along the way, then this will be different: instead you will hop from Town, to Overland map, to Scene. There are plans to also show at least your groupmembers on the Overland map, but the precise implementation of the Overland Map is still in the air.Mostly it will be a fast travel tool, though many players want it to be more like the maps where you can be drawn into battle if you run into a bear and such.
Anyway, I think because of the persistant housing and the no separate-server thing, this will qualify very nicely as a MMO.