There may be a single word for this in the field of linguistics, but my cursory Internet searching didn't turn one up.
I think the most concise (and accurate/precise) expression would be "initial vowel sound word*."
Hey guys, is the word "animal" an initial-vowel-sound word?
(hyphenated or spaced as suits your fancy)
You can find the above phrasing used in ESL/grammar materials and texts. Here is one usage example for reference:
Determining which indefinite article to use is not as simple as seeing whether the following word begins with a consonant or a vowel. The article an sometimes precedes words that begin with a consonant but that are pronounced with an initial vowel sound: an honor, an hour.
Source The Grammar Bible: Everything You Always Wanted to Know About Grammar but Didn't Know Whom to Ask by Michael Strumpf and Auriel Douglas
Note that this sort of question comes up mostly when using an indefinite article before certain "h" words (historical, herb, etc.) and acronyms/initialisms (a/an FBI agent).
*credit to FumbleFingers for jogging my brain with "vowel-initial word" in his comment above