Principle of diode in DRL AND gate
There is more than just logic going on in this circuit due to using that +12 V. If that was +6 V things would be more clear I guess.

Fact is that all 3 inputs are either 0 V or 6 V. When only one of the inputs is 0 it "overrules" the others and pulls the output low. This is the logic AND function. All have to be +6V for the output to be 6 V as well.

Why 6 V and not 12 V?

Because the diodes will not allow it, the output voltage is "clamped".

For there to be +12 V at the output all diodes would have to be non-conducting. This can only happen when all 3 input voltages are +12 V.

Since the inputs are defined to be either 0 V or +6 V, this (all three inputs at +12 V) is never going to happen so the output will never be +12 V. It can only reach +6 V.

well it is not a circuit

What would you call it then? In my opinion a circuit consists of at least two components having at least one common connection. So I'm quite sure that this is a circuit.

And I'm even more sure that Kirchoff's laws still apply.

But rather than "throwing" Laws and formulas at circuit (which I often see beginners do) I look at the circuit and ask myself "What happens here".