mapbox-gl-js version: v0.49.0
browser: Chrome 69.0.3497.92 (Windows 64bit)
raster-resampling paint property of the raster tile layer to nearesthttp://jsbin.com/nohuromeqa/1/edit?js,output
According to the documentation, when setting the raster-resampling paint property to nearest the raster tiles should have sharp pixels when over-zoomed.
Nearest neighbor filtering interpolates pixel values using the nearest original source pixel creating a sharp but pixelated look when overscaled
Also, when changing the raster-resampling paint property to linear the results should appear different.
When setting the raster-resampling paint property to nearest the raster tiles have blurry pixels when over-zoomed.
When changing the raster-resampling paint property to linear the results appear the same (blurry).

raster-resampling set to nearest
raster-resampling set to linear

raster-resampling set to nearest

Interesting! Might be GPU-dependent? Here's how the example works for me on macOS:

Can you also try different browsers?
Ah good question, I hadn't checked other browsers and machines yet.
Here are the results of a few tests:
Looks like Windows vs. MacOS / iOS more than GPU. Are you able to replicate it on a Windows machine?
Hmm, I have no ideas why Windows wouldn't like the NEAREST mag filter. Perhaps you could poke around the code and see if there are any clues? https://github.com/mapbox/mapbox-gl-js/blob/master/src/render/draw_raster.js#L48
Me neither, I'll see if I can find a moment to have a look and poke around.
If it helps, the Three.js examples using a nearest mag filter work as expected (pixellated) on Windows: https://threejs.org/examples/webgl_materials_texture_filters.html

It's passing in the render tests which run on Linux, and I can't replicate this on my Linux machine either, so certainly it being a Windows specific issue sounds plausible.
I can also confirm this issue. I validated that both MIN & MAG texture filters are set to NEAREST using the WebGL Inspector Chrome Extension. This only happens on Windows, no issues on macOS:

Instead of blur, we get rainbowy edges, as we remap grey scale colors of the original tile image.
I did some digging, and from what I can gather, the problematic lines are here:
If commented out, everything looks fine on my side.
Most helpful comment
I did some digging, and from what I can gather, the problematic lines are here:
https://github.com/mapbox/mapbox-gl-js/blob/321a3695a6c068a1cfd58629ed9d8dcb333b8bbd/src/source/raster_tile_source.js#L129-L131
If commented out, everything looks fine on my side.