NES uses a standard SRAM chip. SRAM is basically made of flip-flops that keep the logic state of a bit written to it so the bit can be read back. But on power-up, the flip-flops will go randomly to either contain a '0' or '1' bit, and thus the state of memory contents is random or unknown. Of course it is not truly random, as it depends on transistor manufacturing tolerances and the circuit on silicon will have different leakage currents depending on temperature etc. So each bit will just have a likelihood of being '0' or '1', depending on what the temperature is, how fast supply voltage rises, any noise and electromagnetic interference present etc. But basically, random enough to be called random, but not random enough to be completely random: there tends to be a pattern and given a few powerups, the few bytes that the game uses as initial randomness source could be identical.
Pressing the reset button on NES will do nothing to the SRAM contents; it simply resets the CPU which just starts running code from ROM cart again. If the game does not initialize the memory by writing something to it, then it will be in the powerup state until written.
In all likelihood, the game uses some bytes in the SRAM as seed for the randomness, and that never changes when pressing reset.
There is also at least one game that uses the fact that memory persists between resets by storing contents into memory, so the game can know what state it is in after reset is pressed. At one point of the game, part of the plot is for the player is to realize that there is no way to continue in the game by just playing, and there are hints that the player should press reset to continue in the game and finish it.
