If you read the paper, you'll see that the detail is a little different from the headline claim. In section 6.3 they go through comparing C++ at various levels

If you read the paper, you'll see that the detail is a little different from the headline claim. In section 6.3 they go through comparing C++ at various levels of optimization to equivalent Halide code, and eventually reach C++ code that is faster than the Halide code. However, to do that, even the tuned C++ ballooned from 122 lines of code to 370+ lines, while the Halide implementation was 35 lines, and had allowed them to discover optimizations quickly, by separating the concerns of the algorithm and scheduling. The C++ code is also now very specific to the architecture it's tuned for. So the win here is in terms of maintenance and effort, and the ease of porting to different architectures. Hence, I expect, why they also show comparisons with Matlab.