In short, there is no cap to cut parts and cost, because mostly the board can work without it.
It slightly depends on which exact 78M05 that is and which manufacturer datasheet you are reading.
Even if the 78M05 is a bit special and is said to work without any bypass caps, it means only when conditions are right. Datasheets say that the device is stable without bypass caps, but it literally means nothing if the environment is uncontrolled.
The datasheets still say the input bypass capacitor is recommended or even mandatory, if there is no other capacitance at all, or if there is a long wiring from regulator to the next capacitor, and that "long" basically is said to be 4 inches, which is not that long.
The datasheets do say the output cap can be omitted, but even that requires that the load has no large changes in current.
Well, the MCU is a changing load. It virtually draws no DC current and if MCU runs on a 8 MHz clock then it draws current in 8 MHz spikes, so obviously even per the datasheet the output cap cannot be omitted in this case.
So fortunately the LDO has output bypass caps. And your LD1117 design should have both input and output caps. A capacitor can be omitted if some other capacitors are nearby and can be shared.
So this DesignSpark board is just copying a design that has bare minimum of components for making it work.
But please note that the design is rather dangerous in many ways. If you provide it with external 7V supply and let the regulator provide 5V to the MCU, please note that the board must not be connected with PC through the USB connector.
The board will feed supply current into PC via USB, the diode is drawn the wrong way. If the PC is turned off, it tries to force feed 5V supply into PC, and it might fry a fuse or something else in the PC.
Same thing with the 5V MCU communicating with 3.3V USB data lines protected only by zeners and series resistors. That is living dangerously, one slight mishap and you risk shorting 5V to USB data pins.
But such are hobbyist circuits, bad designs become popular and copied around with no criticism, and users have no clue how careful they should be with a design. I mean, same carefulness should be used if you found an USB stick from a parking lot, you must consider if you trust it so much you will plug it into your PC.