Recent Mario games have been wild and freewheeling, taking the little red plumber on galaxy-spanning trips and global tours, playing with the laws of physics as he jumps between planets or possesses weird creatures with his cap. But New Super Mario Bros is more like the simpler Mario adventures remembered from an early-90s childhood. It has straightforward left-to-right levels set in castles, underwater, on top of giant mushrooms or in the clouds. A loopy overworld connects them all together, offering a couple of different routes through each themed world. You run, you jump, you try not to die. And in multiplayer, where four of you can leap around dementedly together, you help each other out.

But, though the running, jumping, Goomba-stomping and coin-collecting is fun, and the madcap landscapes that you tumble through are endearingly weird, the magic that animates Mario’s best adventures is missing. The music doesn’t stick around in your head for hours after you stop playing. It looks colourful, but oddly flat. After the joyfully creative Super Mario Odyssey, a game that anyone with a Nintendo Switch should own, it’s an unwelcome surprise to play a Mario game that doesn’t immediately floor you with its charm.

Perhaps it’s overfamiliarity that makes New Super Mario Bros U feel a little underwhelming; this is a rerelease of a game from 2012, after all. But even today, Super Mario World and Super Mario Bros 3 feel more exciting to play. This does, however, have the advantage of multiplayer, an experience so enjoyably chaotic that it’s impossible not to laugh. With two players bounding around, you feel like climbers holding on to each other’s safety lines. With four, everyone is pinging all over the screen, fighting over Yoshis. Much care has gone into creating these perfect 2D levels, with their secret crannies, hidden blocks and plentiful golden coins; everywhere you go, there’s a small reward waiting. It encourages the kind of playful experimentation that made early 2D Mario feel so limitless.

Deeper levels reward with fun secrets. Photograph: Nintendo

New Super Mario Bros U – and especially the Luigi-flavoured expansion, which comes bundled with this edition – can be intensely frustrating, perhaps too much so for very young players. Death comes quickly and frequently, and with only one checkpoint in each level, it takes persistence as well as platform-hopping prowess to triumph. I ran through two or three lives on most levels past the introductory world, many more on the hardest, and I’ve been playing 2D Mario for 23 years; the sadistic challenge mode, meanwhile, is a test of sanity as much as skill.

The difficulty is about right for Mario veterans, especially when you’re playing on your own and there’s nobody to rescue you, but it’s not as welcoming to less experienced players. There have been some adjustments to make it more forgiving to newcomers – two new characters make the game much easier, there’s an included stash of tips videos, and kids can be carried through in multiplayer – but it’s still not the ultra-gentle introduction to Mario that it might appear.

The further you delve into New Super Mario Bros U, the more rewarding it becomes. Its final worlds hold some of its best levels, and there are plenty of fun secrets to enliven the second or third attempt at a level. But it’s hard to summon the motivation to devote that much time to it. It’s typically well-made and enjoyable, but next to the best of the Mario series, it’s unmemorable.

• New Super Mario Bros U Deluxe is out 11 January; £44.99