The intent of the restrictions is to avoid "TRAVEL" but still allow recreational activity - the whole phrase "non-essential travel" should be your hint here - outdoor exercise sure, but avoid extended travel.Then why did most states include recreational activity as allowed if we're only talking essential movement here? Do you obey the spirit of every single law when you go chase? If we're just arguing semantics here on following state orders based on terminology, and not debating ethics, then I hope you follow the spirit of every other law as it regards to chasing. Do you speed? Forget to use a blinker? Well you are breaking local and state laws. Again, that is a personal decision and interpretation.
I've been chasing since 2002, and organising my own tours since 2011 - while I might have been speeding in my early days, keeping up with other vans driving for a commercial tour, on my tours I don't speed and I obey all local traffic laws <ask my guests - I always use cruise control on the open roads> - it's actually simpler and more relaxing that way - the time lost dealing with a LEO more than offsets any potential time gained by ignoring traffic laws - just plan your chase targets and leave earlier, so you have slack time to avoid the "need for speed". Of course, when you're in "storm fleeing" mode to avoid risk to your guests, all bets are off on the speed limit.
IMHO, anyone still going out chasing widely in the current pandemic has "lost their moral compass" by ignoring their civic responsibiity to support reasonable containment measures, and not encouraging other people to "find their own exceptions" by ignoring the spirit of the containment measures, and relying on narrow legal arguments to slip through a loophole.