Alex, I am in Taiwan as I read this, going through my backlog of bookmarked articles, and I find this topic fascinating.
You’re right, duìshǒu (對手) is a very common translation of “rival”. In my experience, based primarily on my time spent in Taiwan, it is a versatile term, used to denote friendly competition, as in sports, as well as political-economic rivalry. It is not as harsh as dírén (敵人), or “enemy”. I have also seen tiǎozhànzhě (挑戰者), or “challenger”, used to convey a more specific meaning.
Great points regarding the nuanced differences in connotation between zhànlüè jìngzhēng zhě (戰略競爭者) and “strategic competitor”.