Yama arashi examples from Kodokan Judo Throwing Techniques show sweep
In Toshiro Daigo's book Kodokan Judo Throwing Techniques published by Kodansha International in 2005, which I consider the best canonical source for throw classification, there are two examples of yama arashi and two examples of throws that are explicitly not yama arashi. All of these have tori's right leg very close to or in contact with uke's right leg.
This is Daigo's description of what makes yama arashi distinct from page 77:
Tori places his right calf over uke's right shin and wraps the tip of his right foot around uke's right ankle. In the unique feature of this technique, tori then sweeps up with his right leg placed tight against uke's right leg. This sweeping technique is different from the method employed in harai-goshi.
Both examples of yama arashi involve a leg sweep. The examples are distinguished by tori's right arm position when tori's left hand is on uke's right sleeve.
- tori's right arm on uke's right chest area
- tori's right elbow inserted under uke's right armpit (as in a morote seoi nage)
The examples of throws that are not yama arashi have the same hand positions as the yama arashi examples, but with no mention of a sweep:
- tai otoshi where tori's hands are on one side of uke, on the sleeve and the lapel
- seoi nage with the same hand position as the tai otoshi but with tori's elbow into uke's armpit as in a morote seoi nage
My interpretation is that yama arashi requires a sweep under current Kodokan classification. If there is no sweep, it is not a yama arashi.
In the video referred to by Sjana, the throw shown by Mifune would not be considered a yama arashi but a tai otoshi under Daigo's description. Based on Daigo's explicit counterexample, I suspect the throw in the video may have been considered a yama arashi by some practitioners before, but should not be now.
Kodokan judo throw classification is messy, changes with time, and is not always understandable. Unless you are working for an official exam, it is frequently not worth expending the effort to understand the minutiae.