The original movie titles from 1949 were quite different.
http://www.artofthetitle.com/title/the-third-man/
I suspect that this is a modern font used by Criterion for its re-issue.
Some similarity to Georg Trump’s Signum, digitized as by Canada Type as Trump Gothic Trump Gothic, but much heavier in weight and the crossbars on E and H as well as the bottom of the bowl on R are too low. Or perhaps it's just artwork.
Don

.

Many Criterion DVD covers were done by Kellerhouse Inc.. May be it's one of their many artworks using some bespoke typeface as they're well-known for.
Looks like they artificially emboldened by adding an outline stroke to some Signum-like (thanks Don) font and reworked counters.
BTW, following Don's previous modification guidelines, some more alternatives even if Trump Gothic is a nice find: Proteina, Raleigh Gothic GT, Komu A, Le Gendarmerie 205, Header STF, Heroic Condensed, Movieland JNL, Title Gothic

Thanks Ryuk for the Kellerhouse Link. I find that their use of typography enhances the mood of the Criterion movie packaging.
Don

You might try asking Eric Skillman via his website?

Revised link for Trump Gothic:
http://www.myfonts.com/fonts/canadatype/trump-gothic-pro/
Don