shortest paths algorithm - why backtrack from the end node instead of starting from the starting node?
You want to find the shortest paths $S(s,v)$ to all nodes $v$ (31:30 in the video). In other words, we are interested in computing a function $f(v) = S(s,v)$, and, as explained in lecture, you can write it as $f(v) = \min_{(u,v) \in E} f(u) + w(u,v)$. In the end, it allows you to compute all such values in one go.
If you instead consider an equation $S(s,v) = \min_{(s,u) \in E} w(s,u) + S(u,v)$, you do can find $S(s,v)$ this way. However, you won't be able to find $S(s,u)$ for all other $u$ in the process, and you'll have to run the same algorithm again for other end vertices.