The following holds for the Sony A7, I'm guessing it's similar for other Sony cameras but don't know the DSC-HX60.
The camera has 2 Wifi-connection modes:
(a) AP-mode ("Connect to smartphone"), where the camera acts as an AP you can connect to. Only gives access to JPGs, not raws. API is proprietary but public (https://developer.sony.com/develop/cameras/)
(b) Infrastructure mode ("Connect to computer"), where the camera connects to an AP and pushes any files to a computer on the local network. Uses some MTP-flavour (based on PTP/IP).
I assume you mean (b). You can try gphoto2, which should be able to connect using PTP (however, in the 5 minutes I tried I couldn't get it to work). If you define Linux broadly to include Android, then you can use raw2dng to copy raw files to your phone/tablet - it uses its own PTP/IP stack (disclaimer: I'm the author).
However, for (b), no matter what, you will have to first "pair" the camera to your computer using USB. It's a proprietary protocol that's only implemented in Sony's Win/Mac programs. All it does is to tell the camera to save the MAC-address of the computer. In future connections, the host sends its MAC-address as part of the initial connection request (doesn't need to come from the actual network interface).
raw2dng can take the "paired" MAC-address as an input, gphoto2 maybe as well (not sure - if you want to try, it's the 16 byte UID: 8 * 0x00 + 2 * 0xFF + MAC). So potentially you could pair the camera to another Win/Mac computer you might have access to and then use that computer's MAC address to connect from your Linux box... (untested)