I don't really have a dog in this fight, put down on your app whatever you feel comfortable with.
To answer a few questions based on my experience I'll add this. A CP in a USAFR squadron would not be applying to an airline because they already have an airline job. They are usually one of the most senior, experienced (airline and mil) pilots in the squadron, not somebody in need of resume' embellishment. They do not have UCMJ or G-series order authority (which is a good thing, but that's a different discussion). On the CP's OER/OPR there is a Duty Title "Chief Pilot". This passes muster at the Wing level and above. You are correct, the position isn't described in any official reg, but has existed for so long and is so far spread across the nation that it is considered legit. "Capt America" would not be legit. My theory only, but the position was probably created in the Reserves due to the part time nature of the Sq/CC. Having another designated senior Reservist (not ART) around to make decisions when the Sq/CC was out kept things moving. The duties given to the CP also don't exist in the AD. i.e. Hiring, liaising with civilian employers, mil leave problems, etc.
Another take away-- if you are a Chief Pilot in a USAF Reserve Sq, you are already more than qualified to get hired by an airline, so leave it off your app--you don't need it!