This appears to be the same algorithm used by ripgrep (https://github.com/BurntSushi/ripgrep) for searching when SIMD/AVX is enabled. Specifically, it uses the algorithm Teddy from the library that’s derived from this paper.
https://github.com/rust-lang/regex/commit/203c509df9e1dcba61...
Both libraries also rely on a number of techniques from existing published research.
Hyperscan is ruthlessly optimized for x86 platforms, but has dropped support for non-x86 platforms. Rust's regex crate is designed more as a general purpose, portable regular expression implementation, suitable for wide scale use.
Rust regex is suited to wide scale use. By comparison to Hyperscan, it is not suited to the kind of large scale cases that Hyperscan handles, but it's well done.
Many of Hyperscan techniques are sui generis, not published. Hopefully some of that will be rectified over time.