"Stymy" doesn't appear in Merriam-Webster [0] nor the OED [1]. Wiktionary [2] and Dictionary.com [3] do list it as "variant" or "alternative" spellings, but with no indication that it's an American spelling.
[0] https://www.merriam-webster.com/dictionary/stymy
[1] https://www.oed.com/search/dictionary/?q=stymy