The answer has not been given because it was developed by an external programmer for the the AirNav FS Live Traffic application. Basically it detects when an aircraft meets certain criteria and gives that flight a condition of landing or take-off from a specific airport. For an example if an aircraft is descending at 700 fpm for a certain period of time, is below a certain altitude and the closest airport is London Heathrow then the destination of EGLL is given to that flight number. Depending on meeting the attributes above a variable is added to each flights. The closest it gets to 0.00 the most reliable is the information given.
Thank you for finally answering my question, now that wasn't hard, was it ?
In fact you have also partially answered what was going to be my next question ("why isn't it working ?").
If you'll forgive me saying so, that's a very crude and simplistic algorithm you have just described (and trust me, I know just how difficult it is to fine-tune an airport arrivals/departures detection routine).
However that explains not only why you are missing lots of LHR flights, but may also be the reason why some Gatwick and London City flights are being wrongly reported as Heathrow routes.
To illustrate, I've run some stats for yesterday (20th September):
Of 1135 ADS-B-equipped LHR flights automatically detected by the EGLLADSB website, 118 (10.4%) were listed by RadarBox with either no route at all, or with a route that didn't have EGLL as a From/To/Via.
I know you said you won't publish a route when you have only deduced one of the airports involved, so you have an excuse for some of those blanks, but there are also a worrying number of routes where you must surely by now have detected LHR landings or take-offs for the Flight ID concerned, but continue to list a route between two completely different airports (like those Cathay and United examples yesterday).
I have no reason to believe that the route algorithm is working any better or worse at Heathrow than at any of the hundreds of other airports covered by the worldwide sharer network (Heathrow just happens to be a handy benchmark), so presumably we're looking here at just the tip of the iceberg.
What do you intend to do about it ?