Does this game play like the Might & Magic games 1-7?

It plays more like old classic dungeon crawlers, like Eye of the Beholder or Ultima Underworld, but there are similarities to the MM series. Anyway, one of the biggest differences is, that you're playing in a game world without NPC characters. You'll basically only encounter enemies, like you do in many Hack & Slash titles. There's also not much of a story to Grimrock and no quests in a classic sense. You have to get level by level deeper into the dungeon by fighting and advancing your characters (you control a small party), exploring and solving riddles (mostly due to levers, pressure plates, hidden doors and teleporters) to follow the little story driven thread.

It's very very similar to Dungeon Master, and like mentioned, Eye of the Beholder. So it's a real-time action game, unlike the turn-based MM series, (or at least are usually played in turn-based).