UA very well may give up share in the process. But I would bet you a whole lot that AA will use the 787 on its LAX-Asia routes in order to cut costs and reduce capacity.
Whether AA expected UA to enter LAX-PVG or not, they did and the chances are very high that either one would be doing just fine as the only US carrier. With two carriers in there up against Asian carriers, the market has too much capacity.
The 787 would not only reduce costs but also pull some of the seats from the market which aren't needed.
As for MU, data involving Chinese carriers isn't entirely accurate as you well know but China is one market where US carriers have long had the advantage in picking up the highest quality revenue.
As for the historical dominance of the market, that is precisely the same point that was made about LHR and Latin America when those regions opened up to non-incumbent carriers. Also, countries like S. Korea and Taiwan have had Open Skies with the US for years.
IN Latin America, CO and DL were non incumbents (CO more or less) and the focused on their own strengths which for both has been serving the region first and primarily from their largest and least competitive hubs.
TO LHR, CO, DL, and NW all partnered with AF/KL to gain some strength in the market while DL has since turned to VS to build a presence.
No one is denying the advantage that UA has had to China/HKG and that DL gained via the NW merger to Asia as a whole and the five year headstart that DL has had in starting to move its network from being Japan-centric to focused on each individual market connected directly to the US wherever possible.
IN contrast, AA is trying to build its presence to Asia from the most competitive US gateways and without a major partner from the on the other end of the route.
In Latin America, no one expects AA to be dethroned but DL is aggressively growing - 25% increase in RPMs for the last several months. Perhaps DL is willing to grow Latin America at a loss as AA is doing in Asia; on an annual basis, DL's Latin America system has been profitable at some times of year and not profitable at other times of the year while AA's Asian system has posted heavy losses for quite some time, even while AA continues to grow. UA is growing Latin America at a much slower rate and is generally flat to down in other regions based on their overall weaker financial results.
Again, AA will eventually make LAX-Asia work but they will be subsidizing it for many years to come and they strategically have no other choice but to make LAX-Asia work or have no west coast-Asia presence. Gaining more gates is undoubtedly based on the notion of being able to connect more traffic but I have yet to hear what markets AA can add from LAX that they don't already serve or wouldn't impact flow traffic over DFW or ORD on existing Asia flights.
It remains to be seen whether gaining a few more gates at LAX can give them an advantage in the Asia market but so far AA's financial results to Asia are disproportionately higher than what they should be given AA's overall leadership position in the total LAX market. And other carriers are growing their presence on the west coast including outside of LAX which makes it harder for AA to gain the market position necessary to justify higher pricing power to Asia.