OneFiercePuppy: Grimrock and its sequel come to mind. Personally, I found them quite underwhelming, but they generally reviewed well so it's probably just a matter of taste.
Faenrir: Yep, very disappointed in Grimrock.
@op: Have you tried Might and Magic X ? It wasn't the best game around but i enjoyed it.
Also, another great game that fits most of your criterias and has a first person view (but turn based combat, though): Paper Sorcerer... I reaaaaly enjoyed this one.
https://www.gog.com/game/paper_sorcerer Oh yeah, Paper Sorcerer! How could I forget! It's a really good, old-school modern 1st person dungeon crawlere where you play as the villain, and you summon monsters as your fellow party members (later on you can switch them, but people usually stick to the first ones they've summoned, or switch out one or two members). If you buy it, go and check the GOG subforum for a fix/patch for two important bugs, since the dev never managed to fix them. I've only played the demo but I loved it.
https://www.gog.com/forum/paper_sorcerer/the_latest_update_may_2015_i_believe_thoughts In the meantime I've remembered more modern games of this genre:
The Quest - a really good RPG, originally for Palm PC, the base game has been ported to the PC on Steam now. It's not party based though.
Wizardry sequels - on various platforms, the PS3 and DS, are new Japanese Wizardry games, since they own the license now, but most of them are in Japanese. However some are fantranslated (and fan translations are usually high quality), romhacking or what's the name of the site has the patches for them.
Elminage Gothic: A very hard Wizardry-like game. Or semi-hard, people say it's got some pretty hard mechanics, like aging of characters and stats going down during levels up as well, not just up.
If you have handheld consoles, then you're in for a treat:
For the DS:
Etrian Odyssey 1-3: Very little story, the third game has supposedly the most story content, but classic old-school gaming with teleport traps, warping tiles, holes and so on. (the teleport traps come in quite late in the game, at least in the first game). You also have to make the map yourself, but you can select auto-maping where every tile you step on is filled in (no notes, just that you've been there), so you only have to draw the walls and doors, and whatever else you want. Drawing the map on the lower screen is a big draw of these games!
SMT: Strange Journey: Another classic dungeon cralwer like EO, however this one is darker and you collect demons like in the Persona and SMT games. It is scifi themed.
The Dark Spire: A love letter to Wizardry games, as many reviewers put it, this game even has a classic mode you can switch to where you have 8-bit music and Akalabeth like graphics. Has three endings btw and they unlock consecutively, however at least with the third ending you can continue your normal game to get it. Not sure if you need to replay it twice or only once to get all of them.
Wizardry games, one of them has a partial translation (menus, items and so on). - Japanese language only
Elminage DS: Hardcore Wizardry-likes games, but Japanese language only.
For the PSP:
Class of Heroes 1+2: Basically Wizardry, but with an interesting setting.
Unchained Blades: Cool monster party members and summons!
Elminage Original: A very hard game, not recommended by outlets because of its unforgiving and hard curve.
EDIT: Practically all of these are turn-based, like the old Wizardry and Might and Magic games, since I initially misread your post. As far as I'm aware, Legend of Grimrock, Frayed Knights (which I heard are good and a comedy too!) and few supposedly not so good games on Steam are the only ones, besides single character hanheld games mentioned in the posts below.
Oh, and The Questlord for Android has swipe-based realtime attacks, not sure how good the game itself is. It has a number of good reviews on Amazon and other places.
