I should clarify that the maps mean that this ticket is also not valid for travel via Leeds-Skipton-Hellifield-Carnforth. Again, though, I wouldn't be surprised if your ticket was accepted on these services.
I suspect you can travel that way - the only train to Heysham port is the 10:19 from Leeds via Skipton & Lancaster (arrives 12:57)
NR site is showing up higher fares for travel on that train changing at Leeds - it is cheaper via Carlisle with a 90 minute wait at Lancaster.
Indeed I was thinking that the logical route would have been (if going via Leeds) Newcastle - Leeds then the Northern stopper from Leeds through to Heysham.