I'm not sure I fully understand what you mean by "if you can't do the programming yourself feels like it should be mentioned". PICO-8 provides a code editor where you write everything relating to the game from almost nothing in a subset of LUA, so it's all programming.
As a 'game engine' it only provides the ability to draw basic shapes like rectangles and circles (using code) as well as referencing locations in a sprite sheet and playing sound effects you compose yourself. Compared to some of the big game engines like Godot or Unity, Pico-8 (intentionally) provides way less in terms of out-of-the-box functionality. You can see the API here if you are curious: https://pico-8.fandom.com/wiki/APIReference . If you want something as basic as a start screen that transitions nicely to the game, you'll have to program the state machine that handles that yourself.
I checked out some of the other entries in the jam, and none of them seems to list the game engine as an 'asset'. The game page also already clearly states that it was made with Pico-8 under the 'Made with' label.