I think the implication is that you age slower if you consume fewer calories. So if you adopt CR then you might feel at age 50 how someone on a normal diet feels at age 40, and at 100 you might feel as they do at 80.
I cannot imagine doing every day below 2000 and then going to the gym indeed. That would definitely not be productive and painful, but doing days of weights with 2500 max, other days around 2000 and then some days 0 works fine for me.
I'm trying something along those lines this month - I eat maintenance calories and work out over the week (~3000) and then I eat ~1000 on the weekend (mostly from coffe/milk/protein shake), but I want to do side projects on the weekend - sometimes I can get in the zone and food doesn't even get on my mind, other times I just feel like doing nothing when I haven't eaten.