The link is a good resource, though it skips a few languages spoken among Kara-Tur's empires and kingdoms:
Shou* (spoken in Shou Lung, T'u Lung, Ra-Khati and Tabot)
Tuigan (spoken in Taan/the Plain of Horses/the Horse-Plains/the Hordelands/whateveryouwannacallit)
Wa-an (spoken in Wa)
Kozakuran (spoken in Kozakura)
Koryo (spoken in Koryo/Choson (former kingdom))
Laothan (spoken in Malatra)
The Trade Tongue (Kara-Tur's version of Common, which may or may not be the same as the Common trade languages of Faerûn and/or Zakhara; that decision's up to the DM Team here)
* Shou's spoken form is called Kao Te Shou, and Shou's written form is called Shou Chiang. If you're not concerned with such details, calling the language "Shou" will do just fine.
I'm not sure what language(s) might be spoken in the Island Kingdoms; Kara-Tur's resources don't really have all that much to say about these islands. Even the mysterious jungle kingdom Malatra got its own supplement. The Island Kingdoms got pretty much jack squat, so it's anyone's guess what they speak over there.
For tidbits on languages, culture and overall flavor, however, it might help to think of the Kara-Tur provinces in terms of their analogs:
Shou Lung: Analog of Imperial China. Shou Lung is presently under the Kuo Dynasty (the Dynasty of the Nation) and is ruled by Emperor Kai Tsao Shou Chin. Shou Lung and Wa are the two oldest empires in all of Kara-Tur, and their histories are too long and distinguised to list here.
T'u Lung: Analog of Imperial China's various dissident states (including the more tempestuous Chinese provinces as well as Taiwan and Manchuria). T'u Lung split from Shou Lung during the chaos following the heirless Emperor's death at the hands of the Waan ninja master Fukio during the Omi War. T'u Lung is comprised by an assortment of rogue states who pay mere lip service to Empress Dowager Wai Locunni Eio yet somehow manage to unite whenever faced with invaders from Shou Lung or Wa. The Tsui Tong (a leading criminal organization in Kara-Tur, rivaling the Yakuza families from Wa and Kozakura) has a strong presence here.
Taan/the Plain of Horses: Analog of Mongolia. The Tuigan horse tribes once united under the warlord Yamun Khahan and for years launched innumerable raids against Shou Lung, Semphar, Khazari, Thay and other neighboring nations, similar to Genghis Khan's campaign in our world's 13th Century.
Wa: Analog of Feudal (Edo Period) Japan, governed by a single emperor and a shogunate hierarchy beneath him. Wa's emperor is largely a figurehead, however; the real power over Wa rests with Shogun Matasuuri Nagahide, who has honed the shogunate into a well-oiled machine of commerce and warfare.
Kozakura: Analog of an alternate Feudal Japan, including Okinawa and the Ryukyu Islands; Kozakura answers to no fewer than two or three hereditary emperors, but governance is largely left to a variety of shogun, daimyo and shugo, leading to countless factions and a shogunate weakened from constant infighting.
Koryo: Analog of Korea. Koryo was once ruled by the legendary warlord Wanang Sun, who united three smaller kingdoms and merged them into the Kingdom of Choson (which later became Koryo).
Tabot: Analog of Tibet (like TSR couldn't make it any less obvious...). Tabot separated from Shou Lung when Shou Lung's Shou Ho Dynasty outlawed the religion known as The Way (an analog of our Taoism) and made the Path of Enlightenment (aka. the Eightfold Path, an analog of our Buddhism) the Imperial religion. Monastic orders devoted to The Way fled to the mountainous region of Tabot and made a stand against their Shou oppressors, eventually winning their independence.
Ra-Khati: Analog of Nepal. Ra-Khati borders on the Katakoro Mountains which separate the regions of Kara-Tur and Faerûn. Ra-Khati is very rich in mineral resources, but little is known of their government; some claim that Ra-Khati answers to the Khan of the Hordelands, while others proclaim Ra-Khati's independence from Shou and Tuigan alike.
Malatra: Analog of historical Indochina (Siam/Thailand, Burma/Myanmar, Laos, Cambodia and Vietnam). Though prosperous, the kingdom of Malatra is largely reclusive and mysterious, and tales of great, monstrous reptiles (dinosaurs) roaming Malatra's jungles alternately repel and intrigue explorers.
The Island Kingdoms: Analog of Indonesia, Malaysia, the Phillipines, Hawaii and similar Pacific Islands. The people of the Island Kingdoms are tribal, warlike and xenophobic; what few explorers return from the Island Kingdoms with their lives recount horrifying tales of rampant human sacrifice and cannibalism among the Island Kingdoms.
And yes, Kara-Tur has pirates too. They're called "wako" and they tend to have less style but more savagery than Faerûnian pirates. But they're still pirates.
Anyway, I hope that helps.
Also, I finally made it to the forums. Hi. ;D