frmts directory is not a set of extra packages or plugins (though some drivers are implemented as a plugin if so defined in the makefile), it contains source code for all of GDALs raster drivers. Some are compiled by default, some aren't as they require third-party (sometimes proprietary) SDKs or libraries.
The BSB driver is compiled into GDAL by default (unless it has been disabled on purpose by the OSGeo4W build)
You can see if you have it by calling
gdalinfo --format BSB from your OSGeo4W shell command prompt. You should see:
Short Name: BSB
Long Name: Maptech BSB Nautical Charts
Help Topic: frmt_various.html#BSB
Supports: Open() - Open existing dataset.
Supports: Virtual IO - eg. /vsimem/
Note that BSB support is read-only and you can't use OSGeo4W to install a read-write BSB driver.
What your linked forum post was doing was modifying the BSB driver to allow read-write access and then rebuilding GDAL.
You could do this yourself if you have the toolchain to build GDAL from source. You would need a compiler, such as Visual Studio, and all the development sources/headers etc for GDAL and third-party libraries. However, building GDAL is not easy if you have no experience in compiling native software from source.
If you want to try: