Well, when you think about it, the original started out pretty campy as well. Not to mention the gravitas *cough* and range of expressions *cough, cough* that William Shatner brought to the set.
You mean the Official Angst-Enhanced Pregnant Pause?
(Known in the industry as the “Shat-Stammer.”)
It was only campy in hindsight. I remember watching the series as a kid and not thinking it was campy. The sets were low budget, but compared to what else was on at the time, it wasn't too bad.
Today it looks extremely low budget and campy to us, but I think this series pays homage to the original very nicely. It maintains the look and feel without trying to make fun of it, or taking it too far.
And I-liked-William-Shatner's........Acting-style!