Whether it's rows vs. columns is just a matter of definition, depending on whether you want to propagate the state by left multiplication or right multiplication. The typical definition (in the context of Markov chains) has the rows summing to one. But how to do it is up to the author of the page. Just be consistent.

In my own coursework, that matrix is called a "stochastic matrix", btw, not a "Markov matrix", but again, it's just definitional and not of interest in a simple article like this.

My main point is that summing to one is what you want, and summing to zero is crazy.