As already mentioned, it's a hyperforeignism, just like the /g/ in
Genghis when /ʤ/ would be closer, or the /ei/ in
forte when the French pronunciation actually matches the English spelling pronunciation exactly (mutatis mutandis). When a word is of foreign origin, people like to show off their savoir faire by pronouncing it in a foreign manner--and often make themselves look like fools to those of us who know better.
Over time, these hyperforeign pronunciations become standardized; I may know that French
forte is pronounced /fɔʁt/, but English
forte is now pronounced /fɔɹtɛɪ/. I dare say the same of
Beijing: the hyperforeignism has become naturalized, and however wrong it may be compared to Mandarin Beijing is pronounced with /ʒ/ in English.
(Of course, if you want to get
really technical, Mandarin <j ch> aren't /ʤ ʧ/ but /ʧ ʧʰ/...)