I don't think there's a filter here, per se. The images are fairly dark — one might say "underexposed", although that's subjective — so you'll want to choose exposure settings below what your camera's meter selects. (You can usually use Exposure Compensation for this — dial it down by a few stops, to -2 or -3.) The digital-noise look is a result of high amplification, which you get by... well, not having enough light. One way to do that would be to fix your ISO at 3200, 6400, or higher and choose the negative exposure compensation.
See What is the relationship between ISO, aperture, and shutter speed? if you are ... fuzzy (um, sorry) on the concepts here. In short, ISO, Aperture, and Shutter Speed need to be set together to balance the light available in the scene to get a neutral exposure. You want to set a little bit darker than that, and as noted, you probably want to prioritize bumping up ISO to increase noise. And, if your camera has a customizable "noise reduction" setting, turn that off — or shoot in RAW and disable (or turn down the strength of) noise reduction in your RAW processing software.
You can also do this in post-processing to some degree by using your software's exposure adjustment or tone curves tool to darken the image, and then running a filter to add noise.
And, you may want to save your result as a high compression level (low quality) JPEG as the output — the examples you give definitely exhibit jpeg artifacts, but I honestly can't tell if that's what you like about these images or just something that happened to the examples you found online (where high compression is common to speed transfers and save data).