These specific claims are flaky at best but hard to argue over since anyone can construct enough cases for or against their position to be right enough not to change their opinion of C.
You can absolutely beat C in everything you list. And you also can't. I don't agree that C is the end all be all of performance or code size, except in a handful of cases where there's nothing else available.
C sucks when you need convenience of big standard library or safety above performance. There is nothing like C when you care about speed, memory footprint and efficient memory management. It's great other languages took over in areas C is terrible at but it's not like areas when it's the best and often they only option disappeared.