When 747-400 came out in the first place (in 1989), the closest competitor was MD-11. 602 cm wide, 61,7 m long. Smaller than B777-200, and range 12 200 km.
747-400 has better range than MD-11, bigger capacity and lower costs per seat. But if an airline has requirements which MD-11 could not meet (and therefore the airline needed 747-400), this does not mean A340-300, B777-200ER or B777-300 might not meet those requirements.

The 777-200ER seems about right.
BA bought those instead of more 747-400s and I beleive several airlines went for the 772ER to replace their 747s as they got old.

But the official range of B777-200ER from
http://www.boeing.com/commercial/777family/pf/pf_200product.html
is 14 200 km.

B777-200ER has 412 deliveries and just 19 orders. A330-200, with clearly smaller capacity and shorter range, has 370 deliveries and 163 orders.

What makes A330-200 so much better than either B777-200ER or any model of 767?

I am trying to spot what the problem is with B777-300 non-ER.

Yes, it is big. Longer than 747, actually. The main deck can have 550 seats – a Japanese airline flies over 520 seats on 777-300. It is still slightly smaller than 747-400 or 747-300 with their big upper decks, but quite comparable to the short upper deck 747-100 or 747-200.

And the maximum range of 747-100 is 9800 km. Shorter than 777-300 non-ER. 747-300 range is something like 12 400 km.

How do the costs of a 777-300 non-ER compare against 747-200 on the same route? And if airlines want to decrease plane size, why is 777-300 non-ER not a popular 747-300 replacement?

Sales outcome:
B777-200 non-ER: 88 delivered, still offered but no orders.
B777-300 non-ER: 60 delivered, still offered but no orders.

A330-300: 284 delivered since 1995 or so, 130 orders.

A330-200: 370 delivered since 1998 or so, 183 orders.

Engines found!

See:
http://www.flightglobal.com/articles/2009/12/21/336414/cfm-international-to-provide-engines-for-comacs-c919.html

Comac chose CFM Leap-X for the import engines of 919, so Leap-X shall be built.