Aside from the attack in the article, one might think that VSAT terminals are much more susceptible to DDoS attacks because of their limited bandwidth and the carrier's Fair Access Policy. One might assume that pretty much anyone who wanted to could just send data to the IP address of one and The FAP will restrict the throughput.
The thing is, the commercial VSAT providers have already thought of this. Each terminal is on a private network behind a NAT already, even if you're not using the software proxy accelerator. Incidentally, modern terminals already have the network accelerator built into the VSAT modem, but regardless of this most VSAT terminals are on private networks and can't be reached directly.
Back to the article, the uplink exploit is well-known and several decades old, as another poster reminds us of the 1980 Captain Midnight incident. Even in this case, the best you can do is deny service, and you'll eventually be caught doing it.
At the earth station you're not going to be stealing any data, as it's encrypted on the way down and you're not going to be breaking into the facility.
You're not likely to find them by scanning networks, either, as mentioned earlier most VSAT terminals are on private networks. Even if you were to reach the terminal directly the management port isn't reachable from the outside world, just the private network of the VSAT operator.
The article is an interesting bit of speculation, and has the obligatory mentions of Afhanistan, SCADA, and the SHODAN search engine.