Do I need to replace this tire? Just noticed. The black rubber part feels awfully thin.
The reason that it's important to replace that tire is because the missing piece is part of the tire sidewall. Unlike the rolling surface of the tire, the sidewall is not reinforced by steel belts that make the rolling surface less vulnerable (and easier to repair!).
From looking at that picture, it's hard to tell whether you lost that piece to an impact or whether it cracked and fell off. Both are bad. If something struck the tire hard enough to take off a chunk of the sidewall rubber, the sidewall is definitely mechanically damaged (thus the hole) at a place that's basically just a rubber sheet. If the chunk fell off due to aging, that whole tire is falling apart on the wheel, starting with the weakest part.
I would consider that tire a total loss and expect it to fail at any moment. Please replace it.
Yes, replace this tyre as soon as possible.
That part is weak, not protected and could fail at any time.
Also, you cannot see any internal damage which could cause it to fail while the outside still looks the same.
Replace it - put the spare on NOW.