Oh, it's a Rogue-like, all right; you're tooling around an algorithmically generated ASCII dungeon, moving in eight directions and fighting by running into things. But you're under time pressure: A song is playing, and if you don't finish the level by the time it ends, you lose. Maybe it's a "Musical Chairs-like."
Since you're under severe time pressure, Lait has stripped the UI down to barebones essentials; everything you are likely to want you can trigger with the numerical keypad (zero for "cast spell" and plus and minus for "portals"). You automatically pick and use everything you find, and never bother with selecting which spell, say -- although there are some defaults you can change if you want a particular style of behavior for your character.
And rather than delving ever deeper and finding phat loot and levelling up, each level is a puzzle: You start in the blue room and want to get to the yellow one, before your time is up. The game uses a Jacobian transform (hence the name) to calculate your distance from the target room (in terms of topography, not linear distance), hence the name of the game -- and displays it as text color. You want to head toward the warmer colors, in other words.
Thus, Jacob's Matrix is built on a Rogue-like engine, but the gameplay is about anti-Rogue-like: puzzle-based, and dependent on fast action. Very strange.