After doing some research on mod_deflate and it's usage it may be possible that your implementation of mod_deflate or how it is being called/run that is the issue here, as syntax errors usually mean a typo when editing a conf/ini file (possible use of a word processor instead of a text editor) or, as in this case perhaps, a mal-implementation of a server configuration file entry.
These pages might be worth a read:
Apache Module mod_deflate
Apache Wiki ReInflating
Apache Wiki httpd.conf Example
Also some useful background and other user's experiences with mod_deflate using this Google search
which, among a few other Google searches, gave me some insight into your issue and other issues that may arise using mod_deflate on an Apache Windows Server installation.
BTW libz is not a module in XAMPP but zlib is included in XAMPP as a dll in the apache\bin folder - which may indicate it was included when apache was compiled by the developers.
Not sure if this helps but a while ago (2006) I downloaded the ZipBinaries archive for another project and installed them in a folder I named zip within the apache\bin folder - they included such exe files as gzip, zip and sfx etc.
IIRC they were for use with ffmpeg or perhaps Imagemagik but my memory has faded as to why I set them up in XAMPP now.
I mention the zip binaries because, when researching mod_deflate, gzip (gunzip) was mentioned from time to time.