Well, when you are in the middle of the ocean, you have no fiber passing by and so are forced to use expensive C-band satellite beams that provide very limited capacity, which must be shared with maritime users, prices skyrocket. Having a telecoms monopoly doesn't help here either.
For comparison these are the prices on the other islands Batelco took over from C&W:
Falkland Islands:
http://www.atlantis.co.ac/broadbandrates.html
Ascension:
http://www.atlantis.co.ac/pdf/BBleaflet.pdf
St Helena:
http://www.sure.co.sh/downloads/BroadbandPackages.pdf
The later however may receive submarine cable connectivity at some point which could bring down prices:
http://www.connectsthelena.org/
Operating your own VSAT terminal on DG is very likely strictly prohibited for security reasons, so even if such was more affordable, you could quickly run into trouble.
O3b could help here but with costs of $1m for the groundstation and at least another $1m per year for one of the steerable spotbeams, this is hardly a viable option for less than 3,000 potential users (that converts into $30 per month based on every single soul subscribing). However there would obviously be a signifcant strategic use for such high bandwidth low latency service, which at some point may bring more capacity to DG. The question is whether they would share it for leisure use by the deployed personnel.