Check the Spelling and Grammar settings.
File - Options - Proofing

Actually, I did have 'Mark grammar errors as you type' checkbox selected. I tried both Word 2021 for Windows and Word for iPAD and neither one mark the wording as a grammatical mistake.

UPDATE: I just tried it again with a different machine. It's Word 2016 in a library. Same problem! It didn't catch the grammatical mistake.
Perhaps later version of Word has more lenient standard of what it considers to be a grammatical mistake? It still flags more obvious grammatical mistake like 'I is tired' but not the one shown on the video.