What sort of post production process can help achieve this appearance?
I note that a wide angle lens was used and the vignetting seems overdone, so it could have a strong "postcrop vigneting" (LR calls it that). Secondly, curves have been adjusted for higher contrast and saturations other than red have been turned down, and red has been boosted I would guess (if it is a used subway cart the seats would be much more gloomy). People love local contrast enhancement these days, "clarity", so I bet he used that , too, to make details pop.
I tried these steps on the first random image I found on my HDD that had red in it. I call it a "BWR Image" (black white red image):
Note: I did it in imag view plus more, instead of lightroom, where I dont have saturation sliders per colour. Instead I turned it B&W and drew a "Blendback mask" on the red.
The main thing is it's a high contrast image, and then they've converted to B&W and used selective coloring for the red.
Similar image here How can this lighting/color effect be done? where selective coloring was used.
You can achieve this by shooting in raw, then splitting the image naturally in color channels.
I mean...you can do this...of course with mask and a color image with digitally splitted channels but in RAW or NEF is faster and more accurate.
By the looks of that image, i am most certain that the b&w is raw b&w or it used a camera with advanced configuration to store in-camera-b&w and color in the same time as only one dump from the sensor.