If I recall, Viego is manaless for similar reasons as Yasuo and Yone. The fact that by default, they’re spamming out a really weak ability (their Q) that scales moderately well with stats. And since Viego’s Q is his only form of sustain, even more reason for him to be manaless.
At least, that’s what I recall August saying whenever he was asked. But it’s been a couple weeks since that stream, so I’m not 100% sure if I’m remembering right.
Edit I’ll emphasize that I’m not entirely sure the reasons I gave are the correct ones. I do remember Riot August being asked why Viego was manaless during a stream, and I think he said it was a similar enough reason as to why Yasuo and Yone are both manaless. But I’m not entirely sure if my memory is correct.