There's different textures in differently colored areas. As the questioner told, there's noise, which can be generated in Photoshop's effect. Noise is colored. There's several variations of it combined in a complex way. There can also be used texture photos for more richness.
On the top there's a grey rectangle which has got all-color (=not monochrome) noise with max. intensity. Red channel is just turned to zero with the curves.
In the next image noise opacity is reduced and it has got blending mode overlay.
It adds nothing to light yellow, but blue colors get some noise.
Blending mode dissolve affects like there's noisy layer mask:
On the top there's a solid blue rectangle with blending mode dissolve. A layer mask is inserted. White in the mask keeps the blue color solid. In the top right corner black is sprayed to the mask with a soft brush. The darker is the mask, the more sparse splinters the blue color is
There's again a grey, but this time a big rectangle, which has got as intense as possible monochromatic noise. The result is blurred.
Applying tresholding to blurred noise makes irregular bigger shapes than normal noise:
When dragged to smaller size, it is more like dirt:
It can be used like noise. Here it's used as layer mask of a solid brown color layer:
Painting white to the mask the color gets more solid (left) and painting black fades it (right)
Example 4: Noise gradient
have two colors in 2 layers:
Insert a gradient layer mask to the top layer:
Add a slight amount of noise, do it in the layer mask:
That can already be useful, but now treshold the layer mask to make the transition more grainy:
It's quite same as applying Photoshop's Mezzotint filter to the gradient in the mask.
Try also other Photoshop's grainy texture filters in the layer mask. Photoshop has many of them. You can use also a photo of some dirt. One is easy to make. Rub your hair over scanners's glass and scan a dark paper, adjust the contrast.
Gradient layer mask can make a fade between two different grain textures. In the YouTube theater image example it seems to be used between a texture and its negation.
Example 5 combination
There's no limit here. For example have a grey color layer over the background, add the max amount of noise to it, duplicate the noisified gray and blur the top layer. Let it have blending mode hard light.
Merge the noise layers, colorize it with Hue&Saturation
With or without reduced opacity and varying the blending mode there's again a wide set of new noisy textures.
Hopefully you got some ideas altough there's still a lightyear from these to enjoyable art.