I looked at the answers on SO. I don't think they are satisfactory. People often argue for the normal distribution because of the central limit theorem. That may be okay in large samples when the problem involves averages. But machine learning problems can be more complex and sample sizes are no always large enough for normal approximations to apply. Some argue for mathematical convenience. That is no justification especially when computers can easily handle added complexity and computer-intensive resampling approaches.
But I think the question should be challenged. Who says the Guassian distribution is "always" used or even just predominantly used in machine learning. Taleb claimed that statistics is dominated by the Gaussian distribution especially when applied to finance. He was very wrong about that!
In machine learning aren't kernel density classification, tree classifiers and other nonparametric methods sometimes used? Aren't nearest neighbor methods used for clustering and classification? I think they are and I know statisticians use these methods very frequently.