> is it because the serial ports are not part of the PCI bus?
Yes. Traditional PC serial ports on x86 hardware interface with applications via old-style ISA I/O ports and interrupts.
Keep in mind that RS-232 data rates are down in the kHz range in the vast majority of cases. PCI holds no advantage for RS-232.
Add-on PCI serial port cards may appear in `lspci` output, but that's more about available slots than the appropriateness of PCI to RS-232.