So according to the article, his BAC was measured below the 0.08 limit. They still arrested him. He was likely intoxicated pretty good at 8 PM.
My understanding is the way it works in many states is this:
If you are over the legal limit as demonstrated by a calibrated breath test (not the little breathalizers the cop has, but the big one back at the station) or blood draw and operating a vehicle then that is enough to typically get a conviction for DUI/DWI.
If you are under the legal limit but are still showing signs of significant impairment (i.e., through failing the stupid human tricks) then they can get you for that. Also, keep in mind that alcohol is not the only intoxicant that is typically covered by DUI/DWI. Just because someone is below the legal limit for alcohol at the time they were tested doesn't mean they couldn't also be intoxicated on another substance and rendered unsafe to drive from that chemical, or through a combination of chemicals.
I have no idea in this case whether Alex Jones was breaking the law or not, or if he is being unreasonably prosecuted or not, but just being under the limit doesn't save you from a conviction.