At first glance one might readily declare “game over” in the China online search war. Beijing-based Baidu (BIDU) dominates: According to Jennifer Li, Baidu’s chief financial officer, Baidu’s market share for search in China was about 77% in the third quarter, up from 75.6% in the second quarter.

Google (GOOG), she says, lost share in China, dropping to 17% in the third quarter, from about 19% in the second quarter.

And Baidu is trying to extend its search dominance on mobile phones, an area where Google has done well in China, thanks to a search deal with China Mobile, the nation’s largest carrier. In October Baidu announced a deal to provide mobile search to customers of China Unicom’s (CHU) 3G services, and it also is testing a mobile app that features Baidu’s some most popular online tools, including a message board service.

Surprisingly, Google’s struggles in China have little to do with the quality of its search results in Chinese.

Tech analaysts in China have said Google has done a good job understanding the nuances of the Chinese language. (Google hasn’t fared as well in Russia, where rival Yandex dominates thanks, in part, to its ability to accommodate the peculiarities of the Russian language.) Some users also say Google delivers a better search experience: Baidu had been criticized for mixing ads and organic search results on the same confusing page.

Baidu benefits from incumbent status (it formed in 2000, while Google China didn’t get going until 2006 –after Google sold a modest share in Baidu) and, its executives say, a set of tools that help Chinese users get information – not just search results. A tool called Baidu Post Bar it a bit like a social-networking application that allows users to tap other folks online for advice or comments as they are searching for, say, the best appliance to buy.

But no one, least of all Baidu executives, assumes Google is content with its position in China today. “We don’t underestimate their technology or their ability,” says Baidu CFO Li.

And while Baidu, for now, seems content to focus on search (CEO Robin Li likes to point out that the company’s other services – maps, mail, Baidu Post – all help enhance the search experience) Google’s ambitions in China go well beyond traditional online advertising and search. The company is widely believed to be looking for multiple ways to introduce its Android mobile operating platform in China, and recent reports suggest it may look to open an Android application marketplace in China.

For now, though, Google must live with its second-banana status in China. According to various Chinese news outlets (we can’t find the original document online in English) Google China issued a news release listing the most popular searches in China in 2008.  The most searched term among Google users in mainland China? Baidu.