The post-Cold War relationship between the United States and Russia may now be permanently broken. Although Russia has acquired Crimea, it appears to have lost the rest of Ukraine, perhaps permanently, as well as any sense that the United States will exercise forbearance in the former Soviet space. Moscow wants, more than anything else, the freedom to exercise power in its near abroad, and repeated incidents over the past 20 years have indicated that Washington will not, and perhaps cannot, grant this.
It has been quite some time since Russia would go out of its way to hurt the interests of the United States, but following frustration in Ukraine, Moscow may indeed move towards a policy of open hostility towards the U.S. leadership.
Even with all of the frustrations (on both sides) of U.S.-Russian relations since 1990, most of the players have appreciated the potential of transactional, arms length interactions. The United States and Russia have collaborated effectively on non-proliferation, the containment of Iran and North Korea, counter-terrorism, and the stabilization of Central Asia. But if the deterioration of relations leads to a zero-sum interpretation of Moscow-Washington affairs, all of these transactional interactions could be endangered.
How could this matter for other states in East Asia? Russia could become more intransigent with respect to North Korea, or with respect to its border disputes with Japan, simply because these areas are associated with the preferences of the United States. Similarly, although Russia has historically viewed the growth of Chinese power with some trepidation, Moscow’s hostility to the United States could lead to new frontiers of cooperation between the Eurasian giants.
While Russia rarely relaxes its arms export ambitions for anyone, growing tensions between China and Vietnam could potentially make it harder for Hanoi to acquire Russian equipment. Russia did, after all, slow sales of equipment to Iran at the urging of the United States.
Russian behavior in East Asia is reliable and predictable in the long term, less so in the short and medium. In the long term we can expect Russia to strive to defend the Far East, increase its arms exports, and try to secure a Russian stake in the major multilateral diplomatic venues (such as the Six Party Talks). In the short term, however, these long range interests can manifest in a lot of different behaviors.
Fortunately, the single most critical crisis point in U.S.-Russia relations, the right of Russia to intervene freely in its near abroad, does not apply in East Asia. However much Moscow may want to hurt Washington, Chinese power poses a greater long-range threat to Russian freedom of action. This likely means that as the immediate crisis passes, Russia and the United States will find some grounds for cooperation in the Pacific.