There are several professional solutions for this.
If all you want is to move multiple PCM streams from one system to another, I'd recommend Dante virtual sound card that'll transport 16 channels between systems over an Ethernet network. It maybe possible to tunnel decoded Dolby and DTS using this by first using a software decoder that outputs directly to the virtual sound card. However, I have no experience with this as I've never had the proper setup to try. On the plus side, it is relatively inexpensive.
As far as hardware solutions, there is the Arvus H2-UDMA
that will accept an HDMI audio signal an decode Dolby/DTS to a collection of digital outputs. It is expensive floating between $3k and $4k but will likely work.
Junger Audio I thought at one point had a version of the D*AP8 with an HDMI input which could do the same thing as the H2-UDMA. Due to the modular nature of the Junger D*AP8, it ends up being even more expensive.
All of the above solutions also presume you have proper multichannel input software and recording capabilities on the other PC. There are also dedicated Dante audio recording systems which will capture directly to SD card/bulk storage.