The only God I believe in is ZUN and Rumia can tear my arms off and rip my throat out any day of the week.
Also, I'm not sure about all of the youkai in the series, but Shou Toramaru has been stated to be born from the fears of tigers in stories. I think it was mentioned in one of the official books (maybe Wild and Horned Hermit?). I think, in general, youkai in Touhou are often personified legends/stories/myths. Characters like Rumia are somewhere in the "created through fear" category, but others like Meiling are either born through myth and/or legend.
Either way, no official information so it's hard to say.
It really depends cause some of them are very inconsistent, and there are a lot of entities that fall under the umbrella of how youkai exists but aren't. Most gods are conceived of in similar ways to youkai but a number of them aren't actually youkai but some are. It's easier to think of most of the supernatural characters as "concepts given form" and trying to define youkai in Touhou is like trying to define what is a berry.
Fairies aren't considered youkai in Touhou but are aspects of nature given form. But those who are aspected to seasons, "Letty, Lily, Yuuka", aren't consistent in themselves as Lily is a fairy, Letty and Yuuka are youkai. This is excluding the Aki sisters who are autumn gods of the 8 Million Gods of Shintoism and not youkai. And depending on how a person wants to debate it, Yuuka could very well be a force of nature similar to fairies than a youkai. Who knows at this point.
Then there are the Lunarians (Eirin, Kaguya, Yori, Toyo) who aren't youkai. But the Moon Rabbits, who live on the moon, are youkai.
And it makes even less sense when you start looking through Touhou Lost Word's character tags, which is probably the most comprehentive categorization out there right now, but Lost Word is its own seperate canon and it's tags don't make sense in some places. Like how of all the Tsukumogami (minus Kosuzu, she's just a user of them) are all also one of the 8 Million Gods of Shintoism, but ONLY Kogasa is also categorized as a Youkai. Like, LWpls.