Is 二人 a の-adjective in [今日のサイクリングレースでは、**二人**の選手が最後まで抜きつ抜かれつ一番争いをして いた。]?

Japanese works differently than English. の is used to join two nouns, with the first modifying the second.

• 本【ほん】の読者【どくしゃ】
  book の reader → the book's reader, the reader of the book
• 犬【いぬ】の飼【か】い主【ぬし】
  dog の keeper → the dog's keeper, the keeper of the dog

Sometimes the relationship works out a little differently than the above, in which case you must rely on context and the meaning of the individual words.

For your sample phrase, we have the noun 二人【ふたり】 and the noun 選手【せんしゅ】. The の in between could be possessive, wherein the 二人【ふたり】 and the 選手【せんしゅ】 are distinct and separate entities:

• 二人【ふたり】の選手【せんしゅ】
  two people の player(s) → the two people's player(s), the player(s) of the two people

Alternatively, this could mean that "the two people's player(s)" means the two people are the players. This is most likely the correct interpretation in your sample.

A similar phrase might be:

• 花【はな】の束【たば】
  flower(s) の bunch(es) → a bunch of flowers, where the flowers are the bunch

While の is often used for the possessive, remember that ultimately it's used to join two nouns, where the first is modifying the second.