Reading the article.. It appears to me the woman was likely weaving down the road as she was "Distracted" by the coffee.
Distracted driving is a major issue just now.. Texting, Talking on a cell phone, And many other things constitute distracted driving, Drinking coffee (or water) can be on that list depending on the driver.
That is why the officer stopped her. Her driving patterns suggested distracted driving.
Some other things.. Hanging your Graduation tassel or fuzzy dice or _____ from the rear view mirror (obstructed vision)
Tinted windows forward of the "B" pillar
But in this case it is not that she was drinking coffee. It is that she was drinking anything and as a result her driving was impaired due to the distraction.
Insert story of woman who was posting selfies of herself as she crashed her car here. (True story I might add, sorry I do not have the link).