LDO output voltage lower than expected
The first thing I consider in these situations is load / power and the next is stability.

Parts with a PNP pass element (particularly earlier and less expensive parts) often require a minimum ESR in the output capacitor path for stability.

Here is the simplified schematic for your regulator:



I have added a note about what I do when I see a PNP (or any P type) pass element:

Going to page 22 of the datasheet we do indeed see a minimum ESR requirement:



Given the small size of the parts on your PCB, it looks like they are ceramics which typically have an ESR below the recommended minimum.

That leads me to believe the device is possibly oscillating or otherwise unstable which would render it quite hot in very short order.