What was the value proposition of the 767-400ER over the 777?
The -400ER was a strategic response to the Airbus A330-200
... but it didn't have the range and ultimately didn't sell well.
If you can get the customers who want to replace their DC-10s and L-1011s with the more comparable A330-200 (which entered service in 1998) in talks about the 767-400ER, you have a shot at selling the bigger 777 as well. But if you only have the bigger 777, the negotiations will be harder.
Flight noted the following in 1999:

Anyone seeing the 61.4m (201ft)-long aircraft emerge for the first time could be forgiven for experiencing a certain deja vu. Not only is the -400ER a mere 3.6m shorter than the 777-200, but almost exactly 10 years ago, a similar &quot;767-X&quot; design was being proposed to airlines. This soon evolved into the all-new 777, and for a while the stretched 767 plans were shelved.
(...)
Delta's TriStar replacement competition therefore provided the expected battleground for yet another Airbus versus Boeing fight. Airbus pushed hard to get Delta aboard the A330-200 as part of a wider fleet deal involving widebodies and narrowbodies. Boeing was equally desperate for victory, as much to keep Airbus from gaining a foothold in Delta territory as to launch the strategically vital 767-400X.

I've also put together this derivative work showing the similar length noted by Flight above.