They don't.
Normal people realize that keeping that many photos is a negative value proposition; it's a burden rather than an asset. Rather than trying to hold on to everything, they choose what is actually worth revisiting. This could mean they're a little more selective with the shutter, or they only keep the photos they like.
By all means, keep everything if you want to, but I find it troublesome that storage is considered the problem, rather than making no attempt to cull images. Clearly a great deal of effort has gone into these images to make his various travelogues, so the effort to see which ones make the cut has been done already.
That said, it doesn't seem like a NAS was even needed here. Any reasonable PC MoBo is going to have 6 SATA ports, so you can quite easily make a 4 drive RAID 5. Personally, I just RAID 1 a couple 3TB drives and call it good.