Why isn't just "Nollaig" accepted?
Because an is required for it in Irish. (The same applies to an Cháisc [“Easter”].)
So literally you're saying "the Christmas" and "the Easter?"
Would Lá Nollag ever be used for Christmas, like Oíche Shamhna is used for Halloween?
Yes, Lá Nollag can be used as well as an Nollaig.
I was hoping I can still unlock the Christmas bonus skill