Ruminawi was not eligible for the throne although being son of Wayna Capac and queen (of Pillaro) Choazanguil (source).
Atahualpa was his half-brother, same father Wayna Capac, but by mother had princess (of Quito) Paccha Duchicela.
Both seem to have noble lineage mothers. Why was Atahualpa the chosen one instead of Ruminawi when he was first-born? (And sorry: How accurate are those WP articles on the topic?).
Edit: From the source: era hijo bastardo de Huayna Capac y Atahualpa era el legítimo heredero después de Ninan Cuyuchi y Huascar (translated: was bastard son of Huayna Capac and Atahualpa was the legitimate heir after Ninan Cuyuchi and Huascar). It says somehow that due to being bastard son he was not legitimate heir like Atahualpa, Huascar, and Ninan Cuyuchi were.