No. I'm chinese and i can tell you that's bullshit. "Tiangou" means "sky dog" (or "heavenly dog" if you'd like to be fancy) which is something we made up to explain solar eclipses before modern astronomy exists -- i.e., the sun seems like to be beaten by a dog in the sky, so its missing a piece, thus solar eclipse.
Japanese Tengu are completely different, they take up a large part of ancient Japanese folk culture and is way more than a thing made up exclusively for explaining solar eclipses.
I looked up some japanese and chinese wikis, and they suggest wolf tengus are coming from old white wolves. The wikis also suggest that wolf tengu is an alias of "Konoha Tengu." Wikipedia article for Konoha Tengu explains one of its possible origin is indeed from old white wolves.
See Japanese Wikipedia here (no english version. Use google translate as you wish). Contents mentioning wolf tengu is on the second paragraph of the first chapter: https://ja.wikipedia.org/wiki/%E6%9C%A8%E3%81%AE%E8%91%89%E5%A4%A9%E7%8B%97
I hate to say it, although thouhouwiki seems to be the go-to place for English-speaking audiences for Touhou references, but it's really shit at getting things right. Many of its explanations, background information, origin stories, and common fandoms are straight-up wrong if not missing crutial parts, especially comparing to Japanese and chinese wikis and explainers written by those who would like to dig. There are shit tons of references to china in the touhou series, but this is not one of them. I also do pay respect to those translate touhou games and those building touhouwiki, as they need to look into their references and origins before an accurate translation could be made. Getting touhou translated right is way harder than your average weekly anime. That's also what makes that english patch for IN so infamous as the translators failed to put in efforts to crosscheck, etc.