When valve picked up dota, league of legends was the most played multiplayer pc game in the world. I think it’s more likely that valve was afraid of exodus of pc gamers from their platform.
A bit of both. A group of people in Valve did become fascinated by Dota, though IIRC the leading figure was Robin Walker (of Team Fortress and Team Fortress 2 fame). That's why TF2 started sprouting MOBA-influenced weapons, for instance. But at the same time the business case for adopting Dota must have been quite clear, and surely was discussed seriously. (Valve also had plenty of experience in successfully bringing other people's existing games or mods in-house: TF and CS, Portal and Left 4 Dead.) Meanwhile Blizzard apparently continued to refuse all offers from the Dota developers.