Extracting msi files using Linux

Give msiextract a try, https://live.gnome.org/msitools

And open bugs!

While it won't help you immediately, lessmsi is working on a native Linux version. It preserves directory structure like you want, so it's worth checking up on if this is going to be a long-term issue for you. Unfortunately, .msi support on Linux seems pretty sparse, so lessmsi or msiexec through wine might be your only immediate option, even if (as you said) wine is a pretty heavy dependency for extracting archives.