Shouldn't the "even parity" function map 1101 to 0?
In this context, implementing something as a ROM just means a look-up table. If you want to know the parity of&nbsp;$x$, you put the binary coding of&nbsp;$x$ on the ROM's address wires and the value you read out is the value stored at that memory location within the ROM, which will be either 0 or&nbsp;1.

And, yes, the contents of the ROM that you've quoted are wrong: they seem to be implementing parity in the sense that the output is 1 if, and only if, the input is an odd number, instead of implementing the even parity function.