You can see the ring is broken on the right side.
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Yes - the rectangular hole on the right leads to a curved slot that holds the bolts used to secure your toilet. Your slot is broken which means the right side of the toilet will not be secure. This could (read will) lead to a rocking toilet (not in a good way) which will be followed by leaks (um, eww) and rotted subfloors or worse.
And I'd lean toward a stainless repair kit so there is less worry in the future.
Unfortunately, yes. Look for "toilet flange repair" kits on your favorite search engine or at your favorite big box / plumbing store. Many of them are fairly low profile, but you'll need to be sure you don't end up too high.