Without getting deep into the physics, which I can't claim to be an expert in, I thought I might be able to clarify the meaning behind the equation. The technique is called sum *frequency* generation (or *frequency* doubling if two identical photons are used), so you need to think in terms of frequency, not wavelength.
1064 nm is 2.818x10^14 Hz
1319 nm is 2.273x10^14 Hz
add those together and you get 5.090x10^14 Hz, which is 588.9 nm
1064 nm is 2.818x10^14 Hz
1342 nm is 2.234x10^14 Hz
add those together and you get 5.052x10^14 Hz, which is 593.5 nm
Why add the frequencies? Frequency is directly proportional to energy, so another way of thinking about it is that you are combining the two photons into one and ending up with a single photon with all the energy of the two original photons.
It happens to work out that adding two photons of the same wavelength produces a photon with half the wavelength, but it's really better to think in terms of energy.