The Headlines look like Neutraface.

Yep, neutraface is right - the titles face could be custom? here's another sample...

I guess masthead is a custom work. May be you could start with a condensed sans which shares a similar global design, like DIN (condensed) or Bebas and tweak it. "Only" need to move up or down some crossbars and redraw /R bottom left part (extra work on /M for Bebas and probably longer work on /R for DIN Condensed).

Edit: having a look to your new sample, the slightly tweaked /S (middle transition moved up) could confirm they've started with DIN Engschrift (1451).

I think you're right - looks like they started with neutraface for subtitles and created a complimentary bold caps custom job for the header/main titles. Nice job, not too keen on that S though... thanks for the help!

Clearly not the same but they probably try to follow the same inspiration, a modern interpretation of art-deco font "inspired by travel posters of the 1920s".