While it is definitely admirable to save a car in any form, it is still not up to my taste. And, well, you've said it yourself that it's not for everyone. So I do not like it and that's about it.
The definition of hot-rodding though is not "turning trash into driveable unique cars". The definition of hot-rodding is building dragsters out of old cars. In fact, muscle car can't quite be a hot-rod by definition: it is way too late of a car. Between muscle cars and original hot-rods there are lead sleds, which seem to be a sub-class of hot-rod in the end of the day, but muscle car doesn't belong to any of those two.
Even though a souped up muscle can be referred to as a hot-rod on ocassion - it's not a crime or anything - it's definitely not a hot-rod.
Now, back to the definition of hot-rodding. The original hot-rods were quite simple: people took their factory Ford V8s and Model As, removed fenders, hood and whatever else to make it lighter, and tuned up the engine (or swapped it for a bigger one) along the way. That's the definition of hot-rodding. Turning trash into drivable cars is just restoration and customization, really, and while - once again - it is admirable, the car above has barely anything to do with hot-rods.
If anything, I'd say the Mustang in question is a custom car. Hot-rods and american customs go hand by hand though, and therefore american custom scene is rather prudish. People there really squint their eyes at japanese parts in cars, and any engine that has less cylinders than V8 gets sideway glances. One of the reasons Plymouth Prowler failed in market is because Chrysler made a decision to equip it with a V6.
Using the opportunity, here are some unusual, but classic hot-rods from 1950's. The first two photos is the rather famous Lincoln V12 powered machine, which belonged to Charlie Ryan until his death. Charlie wrote a song about it - named Hot Rod Lincoln, obviously - which went rather big in certain circles.
The later three photos are the Cadillac V16 powered machines. The Dodge survived to our day, which is quite awesome. It is a 1923 original Dodge Brothers' car, pre-dating the factory being bought by either Dillon or Chrysler.
All three cars below is of a proper, most classic shape - and that is what's called hot-rod:
