Whether or not Ibn Ezra wrote it, presumably the introduction, חרוזים על שחוק שח-מת, are from the manuscript. It is interesting that some have changed this quasi-title in reprintings. For example, one has חרוזים על שחוק שקאקי and another is חרוזים על שחוק הסקאק.
Incidentally, the famous interpretation of Rashi on Kesuvos 61b that נדרשיר is אישקקי"ש, or chess, may or may not have any basis (it seems more probable that it was the kind of backgammon precursor nard), but I think the question of the antiquity of the game itself is less important in light of the view that sees the Talmud as developing long after Ravina and Rav Ashi.
See the very interesting letter about chess in Jewish sources in Reggio's Iggerot Yashar v.2 (Vienna 1834), where he refers to other sources, including the איסקונדרי of Kidushin 21b, which Kohut would later interpret fancifully as chess, which he assumes was named after Aleksander the Great. Reggio, incidentally, correctly realizes that the name of the game is Persian, not Arabic, writes מט and not מת.
If anyone thinks Artscroll's translation of נדרשיר as "chess" is silly, I would just point out that Soncino translated it as "checkers." But see the notes.