I haven't read the original paper, I can't comment on that. The model in the webpage however is not heteroskedastic (literally "unequal variance") because all

I haven't read the original paper, I can't comment on that. The model in the webpage however is not heteroskedastic (literally "unequal variance") because all the log-increments are iid. It could be legitimately considered a geometric Brownian motion with stochastic volatility, because the log-error is indeed normally distributed with variance picked from some stochastic distribution, in this case a normal distribution. This term however is normally used for models in which the volatility has more structure (e.g. the ARCH or GARCH models which are mentioned in the page).