Not specific to wasmer, but WASI runtimes are much more lightweight than Docker, especially on Windows or macOS.
For instance on macOS, a wasmer installation is a single 45 MByte executable, the alternative wasmtime is 28 MBytes, and if performance doesn't matter much, the wasm3 WASI interpreter is a 255 KBytes(!) executable - compared to that, a macOS Docker installation is 1.5 GBytes (and that doesn't even include any docker images).
WASI itself can also be used in places where Docker doesn't make sense, for instance in this VSCode extension I'm using a C cmdline tool compiled to a 209 KB WASI blob:
