Is this a spoken contracted form of 現在【现在】？ In this video at time stamp 0:07 the Taiwanese speaker (according to the subtitles) says:

我們現在是在臺北。。。

However the what she actually says for 現在 is one syllable that sounds like /xia1/ to me. 

What am I hearing? Is this a complete other word, or is it a common contraction of 現在?
This happens frequently in oral expressions. Yes, this is a "contraction" as you stated. The context is specific to everybody, so the speaker can shorten some words to express more information. Here the full word /xiànzài/ is shortened as something like /xià(n)ài/, where the sound /z/ and the nasal sound are in fact pronounced but in a very short period, and the recording seems like that the one just omitted /z/, /n/. You could try yourself by reading the word "现在" as quick as possible without altering the leading consonants [or, to be more exact, 声母] the tone and the vowels [韵母], and you might get the same result.