I'll limit myself to the 286 word (!) summary and not RTFA — because Damn! — that's bad enough.
[W]hat actually makes Rust safe, by the way? To put it simple, this is a language with a built-in code analyzer
What makes Rust safe is language design that permits that code to be analyzed. Costly C++ code analyzers that hardly anyone actually uses can't match Rust's built-in, for-free, automatic analyzing compiler because the C++ language itself precludes this.
The rest of the first paragraph amounts to `Rust isn't necessary because C++ is improving.' Anyone that's been watching C++ develop for the last 30 years knows there are both technical and political limitations to how much C++ can ever improve and some people can't wait another 30 years to get halfway there.
Then we get into this drivel;
I can generally understand why it doesn't have a decent inheritance and exceptions, but the fact itself that someone is making decisions for me regarding things like that makes me feel somewhat displeased.
Decent? C++ has `decent' inheritance? I'd be surprised if the author actually understood C++ inheritance. I know most C++ programmers don't. Rust spaces that '80s OO crap and gives you a clean, simple system of traits. You're not limited in any way by that design unless you're employed to write FAQ answers and blog posts about the subtleties of mis-designed C++ OO.
As for C++ exceptions; here is Mozilla's policy on C++ exceptions: "do not use try/catch or throw any exceptions." Here is Google's policy on C++ exception's: "We do not use C++ exceptions." C++ exceptions are broke. Full Stop. These people understand this. The author doesn't.
If the lack of C++ inheritance and C++ exceptions are the best you can come up with to disparage Rust then sign me up for Rust.