I deliberately did not include mechanisms of evolution or fitness in my definition.
Which is why it's a shit definition, if you'll excuse my bluntness.
The purpose of a theory of evolution is to explain the mechanisms of evolution. Anything which doesn't attempt to is not a theory of evolution.
The modern theory of evolution would require a book to explain. My hamfisted attempt to summarise in a brief paragraph would go as follows:
Organisms have heritable characteristics; and the primary mode of inheritance is through DNA. Heritable characteristics which increase the probability of an organism leaving offspring are likely to increase in frequency in a population. The likelihood of leaving offspring we refer to as fitness. DNA replication produces imperfect copies, so new variety is constantly being introduced. Fitter new varieties will tend to increase in frequency. Fitness is relative to the environment, so two populations placed in different environments will tend to diverge,
This seems incomplete, but I was trying to sum up the main points in as few words as possible, and I am not a biologist.
The most popular definition of cladogenesis is the splitting of evolutionary lineages (cessation of gene flow),
At the risk of going wildly off topic - this touches on the reasons why the BSC has also seemed a no-starter to me, and I struggle to understand why it's still treated as if it's the default definition of species - despite it being one that is never used by taxonomists.
Cessation of gene flow can take an extraordinarily long time and, unless physical barriers (like oceans) get in the way, can sometimes take place long after populations have become clearly separated from one another.
Geladas are clearly a separate evolutionary lineage than normal baboons. Nevertheless, hamadryas baboons have been observed to occasionally mate with geladas, and genetic testing has established that this is ongoing gene flow into one of the two populations (it only goes one way, if I remember correctly, due to hybrid incompatibility depending on the sex of the parents).
The article you cite is on the right track, in my opinion. The boundaries between two species are no more meaningful than those between genera and families - they're wholly arbitrary and far too much ink and thought is wasted on them. I think arguing that creationists are wrong because speciation has occurred is a mistake. Speciation has no clear, objective definition.