Someone who's rivalrous is very competitive. It's always exciting for fans when two rivalrous teams meet up for an important match.
If you're rivalrous, you're eager to win, whether you're a rivalrous chess player or a rivalrous entrant in a baking competition. A pair of rivalrous siblings is in constant competition with each other, and a rivalrous presidential contest is particularly heated and cutthroat. Rivalrous is from the noun rivalry, from the sixteenth century rival, which has a Latin root: rivalis, "rival or adversary in love."