Horizontal gene transfer is another way organisms can acquire new traits.
I see the paper says "central tenet of neo-Darwinism that mutations are random...". I'm not that up on neo-Darwinism whatever it is.
(I looked at Wikipedia and it seems neo-Darwinism is the term for the Darwin like thinking of the time so maybe the paper contradicts last years neo-Darwinism but not next years?)
mendel later demonstrated that this variation was passed fractionally, to decendants. this was a conserved probability of fixed combinations [consult "mendels peas" ]
the two taken together resulted in neo-darwinist mechanisms. darwin was not wrong, mendel was less wrong, contemporarily we are still scratching the surface of getting it right, primarily what rules apply to what groups, what mechanisms are conserved, what combinations of functions are served by a particular structure, departing from the one gene one function hypothesis.
current genetic theory is a synthesis, loosely referred to as neo-darwinism