Short answer: Because no one wanted to implement an OS in a game...
Long answer: Most games that required filesystem access used DOS (or later, on 386+ a DOS extender). Since version 2.0, DOS provided good UNIX-like handle-based file system support, and BIOS INT 13h services abstracted disk I/O, so the applications wouldn't need to support different disk controllers and disk types (MFM, IDE, SCSI from tens of vendors, floppy disks, network drives, and so on). While it is possible to implement your own disk I/O driver and a filesystem, it wasn't very practical, as it would mean writing drivers for multiple disk controllers and potentially leaving some controllers unsupported.
BTW, most games didn't use MS-DOS or BIOS when it comes to graphics, sound, and user input devices (perhaps except of mice). The API provided by MS-DOS didn't include any graphics support, and BIOS graphics support was slow (it might have been used to setup a graphics mode, but not to draw the picture). Sound support in BIOS and DOS wasn't a thing either.
