Many songs can build on loops or musical ideas, gradually layering in more depth.
In video games, this can be used to tie in with narrative elements, to convey a sense of progression. Here are just a few examples.
Journey - Tower
In Journey, there is a tower level with multiple floors. With each floor that you transcend, the music adds more instrument layers. It starts with a hum and occasional gong notes, then the occasional cello, building up to a discernible melody with flute and more chimes and percussion layered in.
This contributes to the feeling of ascension. In this case, the progression of the music corresponds with the player's progression in the geography of the level.
Minecraft: Story Mode Season 2 Episode 2
There is a shooting gallery, where the music speeds up as the difficulty increases. The development of the music corresponds to the increased tension and difficulty of the gameplay.
Mario Kart Wii - Menu
Mario Kart is a racing game. In the menus of the Wii version, when you're choosing a kart, track, character and so on, the music layers build up the further you progress through the menus.
This can spice up what might otherwise be considered a mundane part of the game.
Monument Valley: Forgotten Shores
Monument Valley features a princess Ida navigating geometric optical illusions. There is a level where a crow creature has put on the cone hat that she usually wears.
The music starts with a simple ticking percussive instrument upon discovery of the thief. More melodic elements kick in as the level becomes busier with more crows navigating about the space, building up twice. (The instruments with a detuned tang also help to reflect the slight comical nature of the situation.)
When Ida reaches the end of the level where she usually reaches for her hat, the music dies down back to the ticking, when she realises it's not there. Then it turns back into the full-fledged version.
Assemble with Care by ustwogames
When you’re putting back together this watch, the music will become more active as you put more gears back together
Summary
There are probably lots of examples, these are just some ones that I know of. Would love to hear about more.
Other examples I know are kind of similar (e.g. this level in Lumino City where the full version of the music, with more layers, kicks in after you have solved a puzzle, in the washing line.)
There is a slight risk that things become repetitive. But it doesn't necessarily have to be repetitive to give a sense of progression.
Building on existing musical layers as gameplay progresses is one way of tying in music more cohesively with the narrative of a video game.