Trailers, screenshots, and previews of A Little to the Left paint a picture of a tidying game about making things neat – and a cat interferes and cats are nice. That’s not inaccurate, but there’s a lot more going on in Max Inferno’s first game. Presenting you with one-screen scenes of real-life objects like books, batteries, and cleaning products, the game invites you to get organising. The simplest asks are to just make a drawer neat, or straighten some pictures, but it soon becomes more sophisticated, launching into magical realist daydreams of how shadows and stars might be arranged to satisfy some sort of imagined rule set.

And it’s the imaginary nature of the rules that surprises most. Re-assembling a torn picture has a clear and obvious objective, for instance, but what is the right way to line up some pencils? Shortest to longest? Yellowest to purplest? Pointiest to bluntest? There’s no one right answer, so the game will usually accept whatever is your personal intuition – then shock you with the fact that there were other ways of seeing what seemed certain.

More than tidying, the most interesting puzzles are about just being observant: imagining significance in a particular rotation of a glass, or discovering a loopy euphoria in approximately tessellating some things in a cupboard. The mundane is defamiliarised and re-examined, with significance found in the shapes of objects or the way things intersect in the world. Each success is a little greeting of “I think like that, too!” – proof you’re not alone in the universe.

Just as fascinatingly, A Little to the Left manages to create a character for you to inhabit. While the 'junk drawer' is universal, the particular contents of this junk drawer are incredibly specific, personal, and private. Apart from simply browsing the contents of this person's home, you are given an insight into their mind. You might immediately want to arrange their books by height or colour, but how peculiar it feels to discover this invisible person who would order them by thickness. You're not just seeing and touching their belongings, but learning to see them as they do.

But when the hard work’s over, this obsessive spirit is eager, with not a moment’s peace, to sort through yet another mountain of horrendously jumbled buttons or batteries. A new puzzle is exciting, but the fiddliest are a slog to poke through with the relative imprecision of the touchscreen. A screenful of tiny beads can feel like a long road ahead.

Like in last year's other indie tidy 'em up, Unpacking, the intimacy of your role in handling someone's private effects fosters a sense of responsibility to treat them with respect and dignity. This contrasts with purely abstract puzzle games – as most are, naturally – and lifts A Little to the Left up into something a bit more meaningful. At the same time, its irrational but still 'gettable' puzzle solutions, freely offered hint system, and unjudged option to just "let it be" and move onto another scene make everything seem like just a passing thought. Continually renewing daily puzzles also play to that ephemerality.

When it all clicks, A Little to the Left provides an experience that is a weird mingling of the semi-passive and viscerally intrusive. It is only the occasions when tiny touch targets cry out for a mouse pointer that the magic falls away. Once that happens, the plainer, less surprising puzzles aren’t able to carry the show on their own. As a piece, it can’t always sustain its best rhythm, but when it does, it's stimulating, quiet, and memorable.