The Masoretic vowelization here isn't changing the meaning of the consonantal text. The letter ה as a suffix is used throughout the Bible, though less often than ו, to represent the /o/ that marks masculine possession.
Genesis 12:8 אׇהֳלֹה "his tent"
Genesis 49:11 עִירֹה "his donkey" and סוּתֹה "his garment"
Exodus 32:17 בְּרֵעֹה "in its shouting"
Jeremiah 20:7 כֻּלֹּה "all of it"
Psalms 27:5 בְּסֻכֹּה "in his hut"
Psalms 42:9 שִׁירֹה "his song"
Proper names that represent /o/ with ה are especially common.
In First Temple era Hebrew epigraphy, the letter ה exclusively is used to indicate the vowel /o/ at the end of a word, and the suffix -ו in this position is extremely rare, if not nonexistent. For example, you can see that the Lachish letters use this orthography in the words ידעתה, שלחה, בה (letters 2, 3, 5 respectively) and never use ו for this. So a masculine suffix of -ה is actually the older orthography.
The reason for this orthography is that the masculine possessive suffix was historically pronounced with the consonant /h/. This consonant survives in certain environments, e.g. אָחִיהוּ "his brother" (Micah 7:2) and מַעֲשֵׂהוּ "his action" (Psalms 33:4). In cognate languages (like Aramaic) this consonant survives in all environments.
Of course, this isn't to say that the masculine suffix is the only way to interpret a word ending in -ה (in fact, I can see ways to interpret differently the verses I gave as examples by changing the vowels). However, here in Genesis 9:21, it has to mean "his tent." There is no woman or feminine noun that could be a reasonable antecedent to "her tent," so this interpretation would require the word to be referring to something that isn't mentioned by the text at all. Reading the word with a masculine possessive suffix, "his tent," therefore seems to be the best interpretation.