The underlying runtime appears to be Wasmtime, an existing project that you can use separately.
For the system API, Extism supports WASI (a POSIX-like API for WASM) which is already supported by Wasmtime. However it sounds like it also has a different, non-WASI API that provides similar functionality. I'm curious to hear a compare/contrast between these two system APIs, or what motivated inventing a new non-WASI system API. It does appear that WASI is in its early days; WASI was announced in 2019 (https://hacks.mozilla.org/2019/03/standardizing-wasi-a-webas...) but it appears that all of the specific proposals are still early stage and far from being standardized (https://github.com/WebAssembly/WASI/blob/main/Proposals.md).
For the API, Extism provides a C API/ABI that can be called through FFI, but AIUI Wasmtime already has such an API: https://docs.wasmtime.dev/c-api/
Basically I'm trying to understand the conceptual difference between this project and Wasmtime.