We see stocks outperforming things like bonds in the long run (past 100 years), but could this be an artifact of that particular 100 year timeline? When looking at historical return patterns for investments, one can clearly see the stellar performance of equities over the long haul. That being said, we know that we can center in on certain 20-25 year time spans throughout that century where the return characteristics look drastically different.

If this is the case, then couldn't the entire 100 year period demonstrating the attractive returns for stocks be an aberration over hundreds or thousands of years, especially considering how global growth has changed since pre-history? And how could we hope to know? Is there a statistical/probabilistic way to be understand whether our "long-run" returns are in fact indicative of some sort of deep principle regarding average returns in a market economy?
Yes. The relative performance of stocks and bonds depends on monetary policy. Stocks benefit from low interest rates and inflation while bonds benefit from high interest rates. Over the 19th century for example, stocks deflated along with the overall economy while bonds yielded a small positive return.