There's two important pieces of context with Contact that might leave you utterly baffled about the game if you go into it unaware of them. One is that it's a borderline tribute to cult SNES favorite Earthbound, almost to the point of attempting to be an unofficial sequel (even though the *actual* sequel, Mother 3, was released the same year). The other is that it's from Grasshopper Manufacture, the studio run by eccentric auteur Suda-51. Suda didn't write the game or apparently have much to do with it, but pretty much everything out of his studio is highly experimental. So, combine these two factors and a whole lot of Weird For The Sake Of Weird should be expected coming in.
The game mostly draws people looking for an Earthbound-alike, and the overall atmosphere and quirk is certainly reminiscent. But Contact has more meme references, a slightly darker and less playful tone, more obtuse mechanics and less original personality than Earthbound. Most importantly, it also has a much worse combat system, worse area/level design and heaps of really tedious grinding padding out the playtime.
The story is on the thin side, but has you guiding a boy named Terry (or Dickface, or whatever you name him) who gets caught up in a conflict over energy crystals that an evil army wants to use to create superweapons. Terry gets recruited by a dead ringer for Dr. Andonuts, who is constantly present in the DS top screen to dispense advice about the tasks at hand. After his spaceship gets wrecked, he also operates a refitted pirate ship that serves as home base and takes you about the world, which consists entirely of small islands.
To add yet another layer of weirdness, the game breaks the fourth wall in that you, the player, are acknowledged as actually being in control of Terry. The professor usually adresses his communication to Telly, but will make an aside to you here and there. This could have ended up being an interesting narrative mechanic, but it's muddled and underused, and the biggest effect it ends up having is to strip any personality from Terry and turn him into an autonamaton that you're just kind of pushing around.
Another oddball design decision that I felt significantly hurt the game is an insistence on making the entire thing playable with the stylus. It rolls with this odd, almost World of Warcraft-ish battle engine where you don't go to a separate battle screen, but instead press B to draw your weapon, at which point you'll auto-swing at anything you get close to at intervals of a couple of seconds or so. There's some techniques/spells you can spam by holding Y, but battles are mostly just standing next to the enemies in WoW style hacking back and forth until the statistically inferior party keels over. I feel like the main driver behind this decision was probably a desire for 100% stylus control, and had the game implemented an action-oriented control scheme a la the old SNES Quintet games (like Terranigma) it would have been leagues more interesting.
Combat is boring, and sometimes irritating when you fight groups as they can stun-lock you with multiple hits and every hit resets your unseen little ATB counter. But it's not entirely horrible, and the game still could have come off well if environments weren't generally so bland and had little BUT combat in them. A samey pattern quickly develops -- you come to a new island in search of its energy crystal, it's basically a long linear dungeon after an initial small town area, you push in as far as you can until the enemies get too tough, you grind the earlier enemies until they're not so tough anymore, repeat until you run into the boss. There's also basically no real challenge as death does nothing but kick you back to your bed on the pirate ship, complete with all the items and EXP you just picked up, so ultimately the game is nothing more than a test of patience. All this grindery also entails running through the same boring enemy-filled areas repeatedly on each island.
The balance of quirk and charm doesn't come off nearly as well as it did in Earthbound either. The game often crosses the line from being cutely strange to just plain incomprehensible, and the sometimes Engrishy localization leans more toward being just plain confusing than awkward and funny. Earthbound always had strong characters, memorable locations and clear objectives throughout its narrative ... Contact feels a lot more muddled and unfocused.
There's things to enjoy here, like the generally good soundtrack, some of the background art, etc. It's all tied together by a lot of tedium and repetition, however, and Earthbound fans likely won't find the experience is what they were looking for outside of isolated moments here and there.