The thing is, these high-traffic sites spend thousands per month on hosting and have elaborate beefy setups with CDNs, and are renting fat pipes to serve traffic, which in turn DDoS'es the linked-to site in question, and the smaller site is probably running their site off a $5.00/mo Digital Ocean instance and just can't cope with the traffic.
Closer to 30 years old.
(Aside to self: "Where did all those years go to?")
Russians using habrahabr.ru call this Habraeffect.
DDoS is a generic term and slightly similar but usually means something else.