It's difficult to tell from the photo whether or not the audio cableform is screened (with a grounded metal braid) or not, but since the inside of a computer case is such a "noisy" environment from the EMC/RFI perspective, it'll probably make little difference where you route it.
I've tested computers for EMC compliance and had to ask the manufacturer to fit a filtered VGA connector to their graphics output to make good their claims of CE/UL compliance.
If you want true "HiFi" performance from a computer, it's probably better not to use the internal audio cable up to the front panel, but instead make use of the audio outputs on the rear panel.
Better still, consider spending a few hundred dollars on an external USB DAC and remove the audio processing from inside the computer case.
I use a mid-range Cambridge Audio DACMagic 100 connected via a USB switch to four different computers.
https://www.cambridgeaudio.com/gbr/en/products/hi-fi/dacmagic/dacmagic100
If possible, compare the background noise with no music or audio playing and your amplifier/headphones connected to the front and rear panels of the computer and turn up the volume. If you can't hear any difference, then continue using the front audio ports.