Can someone explain today's Dilbert cartoon, in particular explain what "sticking the landing" means?
'Stick the landing' is from gymnastics, when people pull off a tricky move and land neatly on both feet, properly balanced and with a flourish of the arms that communicates 'I did exactly what I intended to do'. It's like a whole-body 'QED'.
stick the landing (third-person singular simple present sticks the landing, present participle sticking the landing, simple past and past participle stuck the landing)
(sports) To complete a gymnastic or other athletic routine involving leaps, vaults, somersaults, etc. by landing firmly, solidly, and flawlessly on one's feet.
(aviation, astronautics) To execute a flawless landing (of an aircraft, rocket, or space capsule).
(idiomatic, by extension) To complete a process in an impressive and conclusive manner.
So in context, the character in green (Who I am gratefully advised by @PatDobson is called ‘Wally’) wishes to spend the rest of his life as a coffee-swilling blob of organic matter.
EDIT: I'm actively choosing not to address what the author may or may not have meant by referencing a DNA test. The test functions as the set up for the joke, and readers may bring whatever sub-text to the idea of DNA testing being used in the workplace according to their own world view without it affecting the joke.
Regarding 'Stick the landing', Spagirl gave a good answer. As for the first square, this is probably a reference to diversity hires. (A recent famous incident of that happened with Elizabeth Warren in 2018: she took a DNA test that showed that she had some Native American DNA which may have helped her advance in Harvard.) Wally appears to be a white male, and as per the first square, does not have enough diverse DNA.
The author has spoken against diversity hires before, so that is my interpretation of what he meant in the first panel. I am not sure how else to interpret "DNA -> do not promote".