I don't think normality is required -- the sqrt(n) scaling factor comes out of variance laws and the definition of the mean.

It should be true for any distribution that has a variance, and the 150-year historic return certainly has a variance.

The sample variance is different from the distribution variance, but I get your point.

Almost, but the distribution has slightly fat tails.

Is it correct to say that makes it (slightly) more like a uniform distribution, if viewed as a spectrum between one-point distribution and uniform?

It's hard to imagine a uniform distribution over an infinite domain, but that sounds right if you're think of it as a half-open spectrum.