Yesterday I took a walk around to take questions about flu shots and was mortified that several of the employees never took their eyes off their computer screens when I spoke with them. 

This is an office, not an operating room or airport control tower. Employees can take a second to look at someone when talking to them.

I also noticed in our company meetings, employees are staring down into their phones texting instead of looking at the speaker.

Is eye contact passe? Are simple good manners gone, too?

I am reading a book on hynobirthing.  The author argues we induce self-hypnosis often in our everyday lives. One of the examples she used was getting so involved in a work project that we get in a hypnotic state.  Maybe this explains your experience. They were in a hypnotic state because of their work ;-)

This happens everywhere.  I doubt it will be going away anytime soon.

This happens everywhere, being employees they cant express their opinion or feeling very easily , so some may take this as an opportunity to express how they feel which out putting themself in a negative position. and i dont think it can be eradicated that easily.