It does have an FM chip. But there are a few versions.
The "originals", let's call them that way, are the Yamaha OPL2 and OPL3 chips. The original Sound Blaster had OPL2, the first Sound Blaster Pro dual OPL2 and with the newer Sound Blaster Pro all cards went with the OPL3.
Now Creative wanted to increase profits / not pay Yamaha, so they made their own chip which replaces the OPL3. Obviously it sounds different, but most people in those days simply didn't notice.
Other companies did the same, some with more success, like with the ESS cards.
So in short, if you want the authentic FM sound, your card needs to have an Yamaha OPL chip.
But for games that use MIDI (and most newish DOS games do), it's not an issue. MIDI (MT-32, General MIDI and AWE synth) were options since games such as King Quest 4, Space Quest 3, Monkey Island, Wing Commander...
It's for games before those that you really want to have a card with OPL chip.
Hence it's often easier to build a second, or a third machine, rather than a single one and always having to make a compromise.