Modern gaming and PS/2 vs USB
PS/2 is an original way of connecting keyboards (and mice) to computers, before USB was created. Apart from the differences I will mention in this answer, a PS/2 and USB connected keyboard will behave almost entirely the same while gaming.
Different protocols
PS/2 uses a different protocol in dealing with actual user input. When the state of a PS/2 device changes (e.g. a key is pressed/released), the protocol interrupts the current task of the CPU and the system immediately starts dealing with the new state. USB on the other hand gets polled, which means the computer keeps asking multiple times a second the input device for its current state.
The good
- This difference in protocols can cause a slight difference in speed,
but it will be so little that it can be neglected for gaming and
other regular uses of a computer.
- As you mentioned in your question, the difference in protocols also
allows for N-key-rollover. But while N-key-rollover means that you
will never run into problems, the 6-key-rollover that USB supports is
almost always sufficient for gaming purposes. (Try pressing 6-keys at
once at your keyboard. You ever did something like that while
gaming?)
The bad
- Because PS/2 interrupts the actual OS, it directly connects to the
system. On older system this meant that removing a PS/2 connected
device while the system was active could cause it to crash. On most
modern system this won't be a problem, but it is still something to
keep in mind.
- Since PS/2 connectors were not designed to be as frequently plugged
in and out like we are used now with USBs, doing this can lead to
bent or broken pins.
Conclusion
So in the end, no, using PS/2 has no benefits for gaming, except for the N-key-rollover that could be useful in some special cases. While connecting your keyboard using PS/2 won't harm your game experiences either, it is probably the easiest to just stick to the protocol everyone uses: USB.
Note
There are other reasons not mentioned in this answer for using PS/2, but these don't make any difference on gaming. For more information I suggest the sources of this answer:
Sources
Wikipedia - https://en.wikipedia.org/wiki/PS/2_port