Nowadays, computers are fast enough so that it is not necessary to include a hardware wavetable synthesizer on a sound card.

As far as I know, the only card sold today with a hardware synthesizer is the SB Audigy Rx, and that only because its main chip happens to be derived from the old Emu10k1 line.

This explains MIDI. Not my video.

Nope, wouldn't consider it hardware under most circumstances.