Is the US dollar losing its dominance? The answer is both A) yes and B) it doesn't matter.

Yes, US dollar is losing a bit of power and influence. This is likely to continue.

Making inferences about the US global dominance based on this fact is misguided. US global dominance is as strong as ever and, if anything, getting stronger. US has very successfully managed to move the game a level above currency, to direct governance via financial, legal, political and military means. It has made any meaningful competitors either entirely irrelevant (e.g. Russia), pretty well aligned (e.g. India) or pretty well contained (e.g. China) It's blue skies ahead.