「Time Word + 限{かぎ}り + で」
means:
"at the end of [Time Word]"
I could not think of another meaning since this is pretty much a fixed expression.
A little more formal and fairly stiff expression with the same meaning would be:
「Time Word + を + 限{かぎ}り + に」
Therefore, the sentence:
「山本{やまもと}さんは今月限{こんげつかぎ}りで退職{たいしょく}します。」
can only mean:
"Yamamoto-san will leave (our organization) at the end of this month."
This would mean that your translaion is much more accurate than the other. Of course, whether Yamamoto is "retiring for good" or going to work for a new organization cannot be known from this sentence alone.