It's an interesting idea, but the way it is introduced ("from vaccines to the Internet, we owe a lot to the probabilistic revolution") suggests that if the normal curve was never discovered that no form of statistics could ever develop. While it's true that historically the normal was studied prior to other distributions, I'm not sure that that would be the only way statistics could develop (but without a time machine that's hard to demonstrate).
A whole lot of statistics comes from the central limit theorem, which involves the normal distribution. Also, many of the other distributions in stats tend to the normal distribution with a large number of samples, so discovering any of those would involve discovering the normal distribution. In addition to not having the basic techniques of data analysis that underly all of the sciences and engineering, we also couldn't have statistical physics without statistics, which means, among many other things, no semiconductor devices.
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