Is this an MMORPG?

[LOL]

Is there big servers with many players?

[Sirius]

Short answer: No.

Long answer:
Still no, it has online play functions and certain player interactions are possible, but this is nothing like a MMO.

[potato]

no

[Lord Bob]

Originally posted by LOL:

Is there big servers with many players?

Adding to what everyone else already mentioned: there are servers, but they're only use is to perform matchmaking, provide messages, bloodstains and check for "invalid" files to dish out multiplayer penalties. Players connect via p2p.

edit: if you check the community hub, you'll see how many players are active playing the game at the moment. Keep in mind the displayed amount of players encompasses all players, meaning even those who don't currently partake in multiplayer.
Regardless of that, jolly cooperation and invasions are pretty active across several matchmaking brackets.