Your answer is the earlier post of the two, by 10 minutes. There are no earlier answers.
The description reads:
Your answer must reach a score of two before any earlier answer to the same question reaches a score of two.
Since you received 2 upvotes and your answer is the earliest (but still posted over 30 days after the question was asked), you received the badge.
fyjham's answer was posted after yours, and because it reached 2 votes before yours did, that user was also was awarded the same badge for the same question. At the time of the second vote, your earlier answer had not yet reached 2 upvotes so the answer qualified as well.
The full description you yourself linked to also says:
- For the purposes of the above rule, "earlier" refers to the submission time of the first revision (source).
where the source link points to a comment by balpha (SE developer) that explains the exact same situation:
When Menachem's answer had two upvotes, Alex' had only one, so Menachem got the badge. Only then did Alex' answer get the second upvote, so suddenly his answer (because it's the older one) was the one eligible for the badge, and thus he got it. While Menachem's answer now isn't eligible for the badge anymore, we don't take badges away once they're awarded. Similar example: If you get a nice question badge, but then get downvoted to only have +9, you keep the badge as well.
So yes, the badge can be awarded to multiple answers on the same question, if those answers reach 2 votes in reverse order of posting.