Competitor does not necessarily mean "enemy."
It is a good question as to whether or not Putin sees the US as an enemy. It is a question of degrees. He might see the US as an obstacle, a variable, or all sorts of other things, but “enemy” is too cut and dried.
The reason most nations have foreign services is because only rarely are other nations totally friendly or totally enemy. But once the label is applied, it creates obligations.
As a competitor, Putin can haggle with the US, cooperate in some things and oppose in others. It is a more flexible position.