Dual DC output voltage power supply made from two power supplies?
This is generally perfectly acceptable.  The only major concern is that of power supply sequencing, meaning ensuring that the various power supplies:


start up in an acceptable order
reach their respective target voltages within an acceptable period of time
start up within a suitable window of time before or after each other.


This is important because an improper power sequence can cause disruptive or damaging currents to flow through the signal lines that connect components that are connected to different power supplies. 
 Sequencing is more difficult to accomplish with two different power supplies versus one integrated system.  You would have to carefully examine the requirements of the various loads to really determine if this is a problem.  

As an aside, I'm not sure why an N64 would need 12V, unless it has a fan, which I don't recall.

Generally you would need to tie the negative outputs of the power supplies together if you need two positive voltages.  It is also possible to use separate power supplies to produce positive and negative voltages by tying the positive output of one power supply to the negative output of the other, provided the negative power supply has no internal connection between its negative output and its chassis/equipment ground terminal.

A major advantage of combining power supplies in this way is that it's easy to create arbitrary sets of voltages and current capacities without incurring the substantial cost of designing and certifying a custom multi-output power supply.  This makes it a very attractive solution for low volume products with high power requirements or requiring nonstandard voltages.

An ATX power supply could work, however given that you need less than 20W, even the smallest ATX supply is going to be tremendous overkill, and will not likely demonstrate good efficiency or regulation.  Also, since most modern PCs derive most of their operating power from the 12V (via point-of-use step-down converters located near the CPU, GPU, and other low-voltage/high-current components), some power supplies sacrifice the efficiency and stability of the lower voltage rails to save cost while providing improved performance and efficiency on the 12V rail.