Well I'm not sure it's a given they stop fighting because he dies. The man had long since become a figurehead - what with his opium addiction and mental illness he couldn't be shown in public.
But putting aside whichever POD causes it, we can analyze the effects. That late in the war there aren't a lot of dramatic changes you can make - not by an earlier Qing victory.
There is one extremely significant linguistic issue though. It just depends on how the Taiping fall. More specifically, when the Taiping lose Nanjing, what happens to it? Historically the city was damaged when it was lost to the Haakaa God-worshippers and harmed still more by the hunger and disruption of being war-zone adjacent, but it was mostly intact right up to the end.
It was the Qing who destroyed the city. Most of the damage was really done by siege; so bad was the starvation that Hong Xiuquan himself may have died of eating grass. For the common folk it was surely a case of outright famine. Then the city was stormed, sacked, and for all intents and purposes ceased to exist except as a geographic entity. Perhaps as many as 100,000 people died when the walls were taken. While the precise number isn't (and can't be) known for certain, in percentage terms it was much, much worse than the rape of the same city by the Japanese in the next century. Westerners returning in peacetime recorded that essentially the entire original population was gone - the city and its surroundings were populated by a mix of recent arrivals who had come in to pick up land and home by squatter's right.
Anyway, back to the language. "Mandarin" Chinese has always been the official dialect of China, but that isn't an entirely useful statement, because there are a lot of dialects of Mandarin, some of which as linguistically disparate as Spanish and Italian. Historically, three dialects have sat the throne as the "real" Chinese - Northwestern Mandarin, Jiang-Huai Mandarin, and now Northern Mandarin. Classical China used the Northwestern Mandarin - the stuff spoken in and around the ancient capitals Luoyang and Xi'an. The growing population of the south and the periodic devastation of the north by war later shifted the cultural center to the Jiang-Huai dialect - that is, Nanjing Mandarin. The language of the court, officials, scholars, and poets sprung from this southern source for at least half a millennium prior to 1864. It's hard to be precise about the timing because changes in spoken language show up very little in non-phonetic writing, but the general rule can be made out from word-order and word-frequency shifts, as well as the contemporary writings of foreigners on Chinese language. After the sack of the city and the general devastation of central China, the capital dialect naturally took over and Beijing or Northern Mandarin has been the standard ever since.
[Side note: Northern Mandarin is one of the more traveled dialects. It actually hails further south in Shandong and southeastern Hebei. Geographically this happened to place it adjacent to non-Chinese areas - northeastern Hebei and Inner Mongolia, Beijing, Tianjin, and of course Manchuria - which were then colonized. It's also spoken in northern Xinjiang because that most remote corner was Sinicized last, after the dialect was the national one. Taken together its "Northern" label is very justified...now.]
If Nanjing survives, though, it's very likely that modern Chinese would remain centered on the Yangtze. Among other things, that might make learning the spoken language slightly harder for outsiders than it is already, as at least in the north many words are differentiated on the G-sound. So chen sounds different from cheng, ying from yin, et cetera. In the south though, the G ending is usually silent. In other words, to a western ear a great many different words would seem to have identical pronunciations.