Lambdas in C++ are almost identical to Rust ones (each closure is a unique unnameable struct containing the captures, with an overloaded operator()), in fact, the current Rust scheme was explicitly inspired by C++11 closures. Historically (C++98), it's true that not much code used closures, because they didn't exist at a language level, but the modern language uses them much more aggressively, even pushing hard on making them more and more flexible (e.g. auto/generic closures in C++14). For instance, sort[1] can take a closure which is more efficient that way than a function pointer, and easier to use than a manually implemented custom type.

Also, closures are just structs with functions that take them as arguments, so if the compiler can handle those, it can handle closures.

[1]: http://en.cppreference.com/w/cpp/algorithm/sort