Almost 10 years since the USB-C spec came out and its great to see a piece of test equipment finally using it. So well done Rigol! That is probably the main reason for the slim design of this new 'scope.
The manual says the power adapter supplies 12 Volts at 4 Amps. First I hope that adapter is complying with the USB Type-C PD spec because I did not see that mentioned in the User manual. Assuming it is complying with the PD spec, 12 Volts is not a required voltage for USB PD to support: 5, 9, 15 and 20 Volts are required (if the wattage is high enough). Next, the 4 Amps is also unfortunate as it is > 3 Amps which means if an alternate cable and power adapter with a USB-C receptacle connector on it are used, then the USB-C M-M cable connecting them needs to have a EMarker chip (or two) in it. If not any compliant USB-C charger will not supply more than 36 Watts (if the DHO 0800 insists on 12 Volts). Interesting to know how the DHO 0800 will react if the power supplied is under what the user manual says it needs (48 W). IMO It would have been better if Rigol had chosen 15 Volts at 3 Amps or better still 20 Volts at 3 Amps. DC to DC converters are pretty cheap with > 95 % efficiency.
Now the USB-C receptacle looks well secured on the PCB from the hi-res photos. What has got me really curious is the little hole on the outer side of the USB-C receptacle on the back cover. Is it for a reset or "set back to factory default" button on the PCB? The angle of the hi-res photo obscures any component on the outer edge of where the USB-C receptacle is mounted to the PCB. Is that hole threaded? The reason I ask is that there are two styles of USB-C "locked" plugs in the spec (but I have never seen one in the wild). The first type has a single screw above the centre, but only on one side. The second type has two screws, one at each end of the USB-C plug. That hole, if threaded, could be for the second type of "locked" USB-C plug to secure the plug (against the plastic back cover) on one side. That would be better than nothing.
Next, can the USB-C receptacle on the back pass USB data? If so, can it pass the high speed lines, or just D+ and D- ? A USB-C hub/dock with feed-through (USB PD) power would be needed to test that. IMO one of the great things about USB-C PD is the usb_communications_capable=0 setting, so USB data capability is not guaranteed.
Finally, why not save a bit more space and put a USB-C receptacle on the front, instead of the USB A receptacle? I'm sure Rigol could supply a USB A receptacle to USB-C plug (male) dongle for pennies for all those USB A plug memory sticks that don't seem to be going away. With 2 USB-C receptacles the issue with one breaking is not "game over" for the 'scope, assuming both ports support USB PD sink capability.