That form is included as a search-only form in the current なぶる entry. That means any user searching for 嫐る will automatically be redirected to the 嬲る entry.
See the entry in question here: https://www.edrdg.org/jmwsgi/entr.py?svc=jmdict&e=2228357
While that form certainly appears to exist, it is very uncommon from the looks of it. Not one of my dictionaries bothers with including that variant form. 新明解国語辞典 is the only one pointing out "「嫐る」とも書く。", which is effectively solved by having it searchable.
Though you can find it in 日本国語大辞典's 表記 section, or various 漢和辞典. But that's not a good criterion.
See also the usage in the google ngram corpus from 2007:
│ 嬲る │ 5,753 │ 30.0% │
│ 嫐る │ 89 │ 0.5% │⇐
│ なぶる │ 13,353 │ 69.6% │
The only two hits for 嫐る in other corpora are in NINJAL's corpus of historical Japanese, one dates 1900, the other 1925.
Tools like yomitan are able to parse 嫐る correctly as well.
Alternative Kanji for なぶる
As noted in an episode of Kyoujou, on Netflix, a show about a strict instructor at a police academy and the various pickles his students get into and often cause, there are two kanji variants of "なぶる” -- one which uses the radical of woman with a man on either side -- "嬲る" -- and the other with the radical of a man with a woman on either side "嫐る" I would propose listing the latter as an alternate writing of "なぶる” in the definition.