Since there hasn't been an official response. If I had to make a guess, I would say they are using a square "casing and backband". Probably a 1x4, maybe a 1x5, with a simple backband around the doorways. The baseboard appears to be a 1x6 with a simple shoe molding (not enough detail in the photo to say more on that). Material is likely either FJP (finger jointed primed) or MDF (medium density fiberboard, primed). It's a beautiful transitional style, lending itself to contemporary design, without requiring the stark minimalist trim detail of a more modern aesthetic.

Darren would you guess that the casing is 1/2" thick or 3/4"

3/4" almost definitely. One of the nice things about this design in my opinion is it provides a definitive shadow line between the casing and baseboard. This eliminates the need for a plinth block or multiple thicknesses of trim. I suspect the base is also 3/4". For what it's worth I'm planning on something nearly identical to this for our own home with 1950's stock builder trim.

http://www.mccoymillwork.com/pdf/McCoy-Catalog.pdf
See the FJP 1021 for the backband, There is some ~1x4 door casing in there as well. I think I'll be using the 1x8 (slightly taller) base, but haven't decided yet for sure.

My current mockup:

Thanks Darren I am also going to be doing a casing and baseboard build like this, have been going back and forth between the 1/2" mdf and 3/4" mdf, I work for a furniture manufacturer so it is readily available for me. I was a little concerned about the 3/4" being a little to bulky for the eye but understand your point about the definitive shadow line it creates.

I used 3/4" casings with 1/2" base at my last house. It worked well. I think 1/2" would look fairly thin next to the backband employed here. But - just my 0.02 USD from an amateur DIYer ;-)

Hi! Great info on your discussion @Guy and Darren but I'm somewhat confused. When you say 1x4 doesn't the 1 refer to 1" .. but then you said the casing was most likely a 3/4". I also love this look and I'm trying to recreate it. Do you think the shoe moulding is square or rounded?

do you think they used a square or rounded shoe moulding?

Hard to tell exactly. But, it looks square to me, due to the sharp shadow lines in the picture