Should this article be expanded to reflect the "ongoing space race" engaged in by Asian and other nations? (No.)
No, for exactly the same reason that
American Civil War should not be expanded to include the 1960-1996
Guatemalan Civil War. The scope of this article concerns an era of history during the
Cold War when the United States competed with the
Soviet Union for preeminence in space exploration. It ended by the time of the Soviet Union's collapse and the end of the Cold War. Subsequent space programs developed by other nations therefore cannot be a part of it, despite journalists' attempts to re-use the term. Wikipedia should cover topics in their proper historical perspective, and their timeless facets recognized by Wikipedia consensus should not be muddled or diffused by recent events; see
WP:Recentism, Latter-day space programs should be covered in other articles.