The strike-out, written down
Write both names in capitals and drop anything that is not A–Z. For each letter of the alphabet, subtract the smaller count from the larger. Add those leftovers. That integer is your step size. Starting at F, hop that many seats around the shrinking list F-L-A-M-E-S, removing one letter each round, always continuing from the next survivor. The last letter names the category.
That is the entire engine. No secret weight for vowels, no gender field, no “seed” that changes at midnight. If two sites disagree, they are almost certainly hopping from a different starting index or cancelling repeats differently.