Wii definitely doesnt make it. Look at any Nintendo system poll, its closer to the Wii U than the next strongest system. The 360 bests it for sure. The NES also does not do particularly well and 80s nostalgia is not nearly as powerful here as 90s/early 00s nostalgia.
I would guess (not counting PC):
Game Boy
Genesis/Mega Drive
SNES
PS1
N64
PS2
Gamecube
PS4
Switch
Dont underestimate the PS4. It nearly beat the PS1 in a 2018 poll - I think the PS4 is much closer to the PS1 than that is to the PS2. The hard part is figuring out handhelds. I think the DS is being massively overrated here, it bombed in every System of the Year poll it had despite massive ownership. By contrast the 3DS did quite well, helped by the weakness of the Wii U Im sure but it actually managed to win one year. Absolutely 3DS>DS, and I think it beats the GBA as well. This is just not a very handheld-focused place. I have Game Boy on there purely due to legacy but the 3DS beats everything after it. The other issue the DS has is that like the Wii its still viewed as part of that casual Nintendo era, which obviously was always absurd but I dont think people here ever came around on that era.
I just decided to change this sig.
Blaaaaaaargh
azuarc