As far as I know – and correct me if I’m wrong, comments are more than welcome – KYODO from Japan is the only service that still broadcasts newspapers in FAX on HF / Shortwave. According to their website they are radio-transmitted twice a day to about 800 ocean-going ships and fishing boats, and hotels in resorts abroad. The first newspaper was published in 1964.
I received them with my RSPdx and MLA30+ antenna on June 26th, around 17:30 h UTC on 16971 kHz. Interesting detail: apparently because of the complexity of the Japanese characters they transmit in 60 rather than the more common 120 lines per minute.
A good overview of the few FAX transmission still available can be found on this website. KYODO has transmissions from Singapore as well.