If you did play Valkyrie Profile on the PS1 or PSP, you should have no issues learning this game. It is a refinement of that formula, not a rebuild. Combat is four heroes, each assigned to an action button, timing attacks on monsters so that items and bonus XP crystals drop. The arrangement of enemies matters, and you can take out many at once if you choose your spots well. Demon's Greed replaces the purification of weird souls as your finisher after chaining strikes, but the mechanism is the same. You can also learn skills by combining the attacks of party members Dungeons are on 2D layers with visible encounters, and defeated foes can be turned into platforms to visit hard-to-reach locations. Outside of battle, you can raise abilities and alter attack patterns to suit your style, and you eventually unlock a class system to allow significant character customization options. There is also a simple item crafting system to allow you to unlock bonuses to your weapons that are either generally useful (e.g. increased HP or attack power) or will help with specific fights (such as extra damage against dragons or poison resistance). The video is of my fight against a mid-level boss.
However much the gameplay is an improvement, the story is at least as big a downgrade. Instead of a web of schemes set in motion by complex characters, you get kids from totally-not-Shibuya with glowy outfits working on interpersonal issues. And yes, of course there is a surfeit of relationship meters. Both VP and EA do have a battle between demons and gods (who will reward you for sending souls and equipment you don't need to them) as a backdrop, but other than the game concealing which side you should be rooting for, there's not much to get you interested in the story.
I've been excited about this game since I first heard about it, and despite not living up to all my expectations, I am happy that I tracked down a copy. If you can get Valkyrie Profile, do so - that's a better game in most respects - but if you can't find a copy of VP or have already experienced it, Exist Archive is worth the time of anyone who values monster slaying over character development.