The parallel port controller can DMA, that lets the driver tell the port hey, send this buffer out to the port and let me know or read this many bytes into this buffer and let me know. It's not peripheral controlled DMA like with firewire or PCI.

You can absolutely exfiltrate data via the parallel port... that's why you attach printers or zip disks... it's just that it needs host participation.

It’s almost certainly impossible on modern systems. The southbridge which allowed DMA to parallel port was absorbed into PCH and slowly stripped of legacy LCP support by chipset and motherboard manufacturers.