Ok, I had a few minutes to take a quick look and thought I’d share my first impressions.
When I look at color tones that I like, I often focus on a couple of specific regions first. I find that it often gets me quite far along the way, particularly with these types of images. So, looking at the same one others have posted:
The first place I’ll usually look is the shadows (and deep shadows). I’m usually looking for areas in the image that I would expect to be black or near–black.
For instance, have a look at the sky in the sample image. I would expect the color to be black(ish) normally.
Values
If I look at the histogram of the image, I can see this:
Which shows me a hard cutoff around 20 on the blackest tones. This is a common technique for those looking to add an “analog film” feel to their images - faded (lifted) blacks.
- Lifted Blacks - raising the output levels to abruptly cutoff the tones earlier than full black.
- Crushed Blacks - increasing the black levels and destroying detail in dark areas.
Sometimes, people will use a combination of these two things in an attempt to emulate what they think analog results should look like. To show an example on your test image (done in GIMP):
These black tones have been crushed by pulling the black point darker (and putting an anchor point in the curve to minimize shifts in midtones and above):
These black tones have been lifted to decrease contrast and remove true black from the image:
When done together, the details are killed and the results lifted all at once:
It appears from the histogram of Masashi’s image that he has at least lifted the darkest tones. There are still some details in those tones - so he may not have crushed them first.
Takeaway: lower contrast in darkest tones, lift their values from black to a dark grey.
Colors
Dark
The color toning isn’t too much trouble to get close to. First let’s see what might be going on. I took a look at the sky in the upper part of the image where I would expect it to mostly be either black or really dark (it’s been lifted, but the I’m more concerned about the color shift away from black):
My sample points in GIMP show some interesting color shifts in what is supposed to be really dark/black tones:
Reds are ~10
Greens are ~35
Blues are ~40
If we assume the sky was likely a neutral dark color, then the differences in the RGB channels give us our dark color toning (blue/green heavy). Greens and blues raised approx 25-30 above red.
Light
Looking around I checked a couple of places that were lighter (to lightest) in the image. They showed a consistent lack of blue in the places I checked (the bright signs, inside the shop, a wall). I assumed these areas should have been white, but could be wrong - so check multiple places if possible.
This time, the blues are significantly suppressed in these tones by 80-100 vs. red and green.
Teal and Orange
Which means we are quite close to a classic Teal and Orange color grading that might be abused in cinema movies. There’s maybe a bit more green-ish hues prominent in the shadows, and the highlights might trend towards slightly yellow-ish, but overall the idea is the same.
Grading in darktable
There’s a couple of different ways to approach this in darktable off the top of my head*.
(*disclaimer: I am no darktable expert - so please heed those who know way more than me).
Split Toning
There’s actually a split toning module that you can use to directly modify the shadow/highlight toning and achieve similar colors:
You’ll basically have separate controls for shadows vs. hightlights, and can adjust hue/sat for each. Balance let’s you shift the middle point between them, and compress controls the amount. You can, of course, further dial it in by using masks.
You’ll still need to lift the blacks in a separate module. The easiest to do is probably the tone curve module, as you can adjust the L channel similar to how you would value in an RGB curve editor (we’re coming back to this shortly). Make sure the scale chroma option on the tone curve module is set to manual, or dt will try to scale the chroma for you automatically.
If you simply want to lift the blacks, you can pull the black point up on the L curve:
If you also wanted to crush the blacks, you can put a small curve near the bottom as an anchor to bring the other tones back to normal-ish (you should see a loss of details in the dark tones):
Color Correction
The color correction module also let’s you adjust these tones very quickly (and intuitively - man I love those dt guys sometimes). In this case, you can specify a light and dark point by clicking and dragging - here I pulled the lights to yellow/orange, and the darks to blue/green/teal:
What’s neat about this module is that the mousewheel will adjust the saturation for you, which is a nice way to slightly desaturate the image at the same time.
You’ll need to lift the blacks using curves again.
Color Balance
There’s also a Lift-Gamma-Gain color balance adjustment (whee!). I like this because it is the same approach a cinema color grader may use. At least the terminology is similar. 
In this case, the lift controls the shadow/dark tones, gamma the mid-tones, and gain the bright tones (roughly). Knowing that you can fiddle with the color balance of these regions (along with their factor). Here’s a quick try:
You will still need to lift the blacks with tone curves.
More
I was going to continue talking about using Lab curves as well to do this, but honestly, these methods are already awfully powerful at achieving the same base color toning you’re looking for. I’d start with these first.
In the end, here’s about a 10 minute try by me fiddling with color balance + tone curve (to lift blacks):
We can probably do a bunch more with a proper raw file. It feels like there might be some tonemapping going on in his image, but not 100% sure. There’s also some saturation bumping that’s happening I think (or Japan is just a really color-saturated country?). (I see you posted a raw file while I was writing this… I’ll grab it and give it another go).
Here’s my dtstyle from the above fiddling:
Leonidas-test.dtstyle (909 Bytes)