The existential risk stuff was baked into the Effective Altruism movement from the beginning, founder William MacAskill was a student of co-founder Toby Orb who

The existential risk stuff was baked into the Effective Altruism movement from the beginning, founder William MacAskill was a student of co-founder Toby Orb who in turn was a student of Nick Bostrom, who established x-risk research as a field in academia. Orb and Bostrom both now work at Future of Humanity institute, an institution dedicated to the species' long term future, and it's mostly concerned with x-risk research. Both Ord and Bostrom are frequently cited in EA writings, with book clubs being organized around Ord's doomsday warning for popular reading The Precipice. Bostrom and Eliezer Yudkowsky knew each other from their early transhumanism roots, and some of the early EA community organizing was done through his LessWrong forum. That and the establishment and funding of both EA and Rationalist orgs in Berkeley by philanthropists associated with both causes, primarily Skype co-founder Jaan Tallinn, seems to explain the overlap between those communities (fun fact: the Effective Altruism online forum runs the same custom software as LessWrong). And of course Eliezer has dedicated his career to funding AI x-risk institutions.