Is this circuit risky for an Arduino Uno?
That circuit is fine as long as the input signals don't go above 12.5V.  You can protect it further by adding a 5.2V zener diode across each of the signals as they enter the Arduino:



simulate this circuit &ndash; Schematic created using CircuitLab

Why is this circuit not going to burn my Arduino if it is using 12V?

Because it uses a voltage divider to reduce the voltage to 4.8V.