The article says "We compute the hashcode of the entire graph by hashing the multiset of WL labels. With one round, we’re just comparing the degree histogram. The more rounds we add, the more likely we are to detect a symmetry-breaker:", which is not correct.
Repeatedly re-labeling a graph by assigning a unique label to each unique neighborhood histogram, until the corresponding partition reaches a fixpoint would compute the one-dimensional Weisfeiler-Lehman refinement. But there are many non-isomorphic graphs that you cannot tell apart with this! It cannot tell apart any two regular graphs of the same size and degree, and you can easily run into those in practice.
Even if the code would repeat this process until a fixpoint is reached, instead of hoping that 10 iterations suffice, non-isomorphic graphs that result in the same WL partition means that "The more rounds we add, the more likely we are to detect a symmetry-breaker" doesn't hold.
There are also more efficient ways of computing this.
Now apart from one-dimensional WL refinement, where you compute a label from the neighborhood of individual vertices, there is also k-dimensional WL refinement, which very roughly speaking looks at all length k sequences of vertices and computes statistics for those. Here it is true that as k reaches |V| you will be able to tell apart any two non-isomorphic graphs, but only because if k=|V| you're trying all permutations! There is no fixed k that will tell apart any two graphs.
If you want to perform graph isomorphism tests in practice, I'd recommend Traces: http://pallini.di.uniroma1.it/
It combines two-dimensional WL refinement with a recursive search to tell apart all graphs, while using computational group theory algorithms to efficiently prune the search space for graphs with many symmetries. It is very efficient in practice.
It is described in https://arxiv.org/abs/0804.4881 (also linked from the website) and also has references for everything I wrote (modulo any mistakes I made while summarizing).