English Translation
This is the room he rushed into.
I did analysis of this sentence and the particle が should be after 彼 (kare) because it serves an essential grammatical function by marking 彼 (kare/“he”) as the subject of the action verb 入った (haitta/“entered”). This subject marker indicates who is performing the action in the relative clause that modifies “room.”
Without the が after 彼, the sentence would become grammatically ambiguous or incorrect because:
The subject-verb relationship wouldn’t be properly established
It would be unclear who performed the action of “entering hurriedly”
Japanese relies on these particles to create grammatical clarity since word order is more flexible than in English
This is similar to how English uses word order to identify the subject, but Japanese uses particles instead. The が particle is particularly important in complex sentences with embedded clauses like yours, where it helps listeners/readers track who is doing what within the different parts of the sentence.
Maybe a native Japanese can give their 2 cent like user Ms.Fixer, to check what the analysis told me. Mam, if you see please give your opinion or anyone with great command of Japanese.