If you're asking if it can be used even if there isn't actually any competition involved, I would say that might not be a natural usage of it.
https://dictionary.goo.ne.jp/thsrs/8859/meaning/m0u/%E3%83%A9%E3%82%A4%E3%83%90%E3%83%AB/
I think only the first meaning is the "correct" use. Many people may assume that just because you are in equal strength for example, you are rival/competitors, so they will use the term close to the meaning of "relatively equal in strength". But the person themselves might not think they are rival just because they do the same thing with equal skill (e.g. they are not competing) so they won't use the term ライバル to describe themselves.
The meaning
Does this mean “rival” only as competitors or can it also mean “rival” as in relative in terms of strength.