It also works on transatlantic routes. In the previous "long haul challenge" I was based on the US east coast and there were people flying A380, 747 and 777 to all over Europe. They filled the demand very quickly of course. The only counter-measure in this case is to "win by frequency".
Your example: 3200 demand, ~10x 777 flights with ~350 seats = 3.500 supply
You may think the route is filled and you got no chance. But wait. You can (and will) win by frequency. Simply pick a longhaul aircraft with 200-250 seats (think A300, A310, 757, 767-200) and fly that route various times. Let's say 10 times. There will be 20 total flights (10 of yours and 10 of your competitor). Devide the 3200 demand by 20 flights and you will get 160 pax per flight. Your A310/757/767 is pretty much full (at least profitable) while his 777 will be less than half full (and not profitable). Repeat that with all his routes and he'll be gone sooner or later.
Again, this is only a rule of thumb. It still depends on fleet choice, seat config, pricing, scheduling...