Super Monkey Ball Banana Mania: Don't get Banana Blitz HD, the camera controls suck. If you're unfamiliar with Monkey Ball: Monkeys in balls navigate puzzles to get from the start to the finish in as little time as possible. Originally an arcade game. Sponsored by Dole, the banana people.
Tetris Effect: It's Tetris! With lots of shiny colors! I'm not the hugest fan of how they set up the grading system, but it has lots of replay value and has lots of no-fail modes.
Abzu: Somber, deep, with bright colors and lots of fish. A little eerie in places. No dialog/words.
Journey: Possibly a little mature (despite its Everyone rating) for how eerie it is, Journey contains no words. There's spoken dialog in a language that nobody knows anymore. [2] reviews.
Offspring Fling: You're a momma fluff who's gotta get her little fluffs home! Very little penalty for failure, it's a fun sidescrolling platforming game. A few spots might need help from a parent to get right.
Echochrome: Think MC Escher, but as a perspective puzzle game. PSP/PS3 only, though...
Do you read to your daughter? If she's got the basics of words down and you want to work on words being read, heard, and having meaning, I have some suggestions!
SkateBird: BIRBS! TECH DECKS! Heckin TRICKS! There's story, told in birbish. The difficulty can be turned to super low, the assists turned up super high. There's very few "big words" anywhere -- most of them are maybe two syllables, and the story revolves around "Big Friend". The whole first part of the adventure is cleaning up Big Friend's room. You can customize the bird you play as. You can, in fact, pet the bird.
Pokemon Mystery Dungeon: Rescue Team DX: Pokemon, but with a focus on... the pokemon? Yeah it's an RPG, and there's fighting (like any pokemon game), but it has just enough plot that you'll be able to read for your daughter and help her along. [1] reviews it.
PIKMIN 3: It's Pikmin, there's really nothing else to say. It's cute, it's teamwork, but beware: There's a lot of (vaugely useful) dialog.
Katamari Damacy: Not super recommended, but worth a try if you're not familiar. The king of all cosmos has gotten himself "one with nature" (read: drunk off his petard) and dumped all the stars outta the sky. Lots of colors, but the difficulty curve is tough for a 4yo. Also there's a loud siren at the end of each level as you run out of time that spooked me the first time I was playing it.
Here Comes Niko!: You're Niko! Your goal is to make friends! Dialog-heavy in places, but with a little adult help, definitely doable!
The Unfinished Swan: perhaps a bit artsy, give it a glance and see if it's something you and your daughter would enjoy.
[1] https://youtu.be/qrvRbKiLZKI
[2] https://www.gameinformer.com/games/journey/b/ps3/archive/201...