Lords of the Fallen
Lords of the Fallen was made by Deck13 Interactive and CI Games, and was widely advertised as a Souls-like game with a heavier emphasis on story delivery and character development. While it does deviate from the Souls formula quite a bit (talking protagonist, less freedom in class upgrades and development, etc), it’s undeniable that this game was rather heavily inspired by Dark Souls.
No auto checkpoints: Check. Each time you die, you restart at the last ‘safe place’ you rested at.
No map: Check.
Lose ‘Souls’ upon death: Double check.
Has a stamina bar, rolling, and blocking mechanics: Yes. Check.
Exploration and shortcuts: Well, Lords of the Fallen certainly isn’t as well-designed as the Souls games, and the areas definitely aren’t as interconnected as you’d expect from From Software’s titles. But the exploration is there, so yes. Check.
Tough bosses that require learning of patterns: Oh yes.
Is it Souls-like? Lords of the Fallen managed to check all six requirements, so yes. This is a Souls-like game.