This is the first I've read this particular take, but I got about the same from my recent read of "The Hobbit". This is, at the least, heavily implied.

There's clearly a past relationship, causing loyalty, and it specifically follows the Took bloodline.

I'm sure there are other explanations than Gandalf loving and sleeping with a Took sometime in the past...but there aren't really any simpler explanations that include the familial (possibly genetic) aspect.

• Gandalf always checks in with Took family members, and has done so longer than anyone can remember.
• Took family members tend toward an adventurous spirit that defies explanation in their Hobbit culture. Took family members tend to leave home, return wealthy, and say very little about their time spent away.
• Gandalf only takes an interest in Bilbo upon learning that Bilbo has Took bloodline.
• Various characters criticise Gandalf's involvement with Hobbits in ways that maybe have "there's more to this" undertones. This one is iffy, there's always "more to this" with Gandalf, anyway.
• Everyone knows Gandalf loves Hobbit....smoking weed.

It could really be as simple as Gandalf and a Took Hobbit ages back had adventures and became practically brothers/sisters in arms. Perhaps Gandalf owes some kind of oath to a dying Took. But it doesn't feel like an oath in the books.

Gandalf acts like distant family.

But there's undeniably an awful lot of "Gandalf acts like an agesless great great grand uncle to all Tooks" going on.