Seemingly not much info on the internet about what a lightning strike point on open ground would/should look like.
If that is what these are, you may find a 'fulgarite' in the middle of them (where the silica in the soil has been fused together into a root-like structure).
Campfire sites you'd expect to be in places of shelter, and you'd find part-burnt wood (etc) that had obviously been bought in to the area.
Were the marks on more elevated areas?
They may be sites used as ignition sources for 'swaling' :
http://www.legendarydartmoor.co.uk/swaling_moor.htm but it is the wrong time of year for that if some of them looked fresh.
There have been some dodgy goings on on Dartmoor (involving burnt ground) linked to satanic activity, so perhaps these are left over from rituals?!