program.cs

class Program
    {
        static void Main(string[] args)
        {

            var words = File.ReadAllLines("words.txt").Select(x => new Word(x)).ToArray();
            var candidate = new Word("ethylenediaminetetraacetates");

            var watch = new Stopwatch();

            watch.Start();
            var matchedWords = words.Where(word => candidate.Contains(word)).ToList();
            watch.Stop();
            
            int wordCount = matchedWords.Count;
            
            Console.WriteLine(wordCount + " words found in " + watch.ElapsedMilliseconds.ToString("00.00") + "ms");

            File.WriteAllLines(@"c:\temp\ethylenediaminetetraacetates.txt", matchedWords.Select(x => x.Original));
        }
    }

word.cs

    public class Word
    {
        public string Original { get; set; }

        private int[] _alphaIndex = new int[26];

        private int _letterFlag = 0;

        public Word(string s)
        {
            Original = s;
            foreach (var ch in s)
            {
                var ndx = ch - 'a';
                _alphaIndex[ndx]++;
                _letterFlag |= 1 << ndx;
            }
        }

        public bool Contains(Word other)
        {
            if ((_letterFlag & other._letterFlag) != other._letterFlag)
            {
                return false;
            }
            for (int i = 0; i < _alphaIndex.Length; i++)
            {
                if (_alphaIndex[i] < other._alphaIndex[i])
                {
                    return false;
                }
            }
            return true;
        }
    }