What is this formula, related to simple linear regression, called?
I do not know other terms than the  average of inverse slope or the inverse of the harmonic mean of slopes. This is also the negative of the average slope of the perpendiculars.

It gives you the inverse of the average slope of lines passing through $(0,0)$ and $(x_i,y_i)$. If the $(x,y)$ are almost aligned with $(0,0)$, this is an estimate of the inverse of the slope of a line passing through the points. 

Linear regression is quite different, as it involves cross-products of sums of $x$ or $y$.