That's not what I was planning either, but that system wouldn't be any different from the current one as long as unvoted games got -9 points. It's only done the way it is now because it's a lot simpler to compile the data.
What I'm thinking is something like... basically, the more votes a game has, the less each individual vote counts - so at the higher ends of the ranking, the average rank of each vote would matter more than the amount of votes a game gets. I'm probably going to have to apply a similar system for something else I'm planning on doing, but I'm not sure if it's the perfect or the worst time to implement a change on the final results.
You say it's always been an issue, but I've been here since 2014 and nah, it was never as Nintendo-heavy as it's been in the last few years. 2018 was thankfully slightly less Nintendo-centric than 2017, which had Mario Kart 8 at #5 (disgusting), but still pretty bad. It's obvious that Nintendo will always have a heavy presence in such lists, but it's been too much, and it's clear that games such as Mario Kart 8 only make it as high as they do because it's basically everyone's go-to Mario Kart game to list, so it gets loads of votes but rarely does it make it to anyone's individual top 10. It's just not as impactful of a game to most people, but it is one that's almost universally liked, and it's okay for the results to prioritize that, but it's making the list increasingly predictable and boring... and most importantly, alienating to some people.
To use an example of a game I personally love, Hollow Knight nearly made it into my top 5, but it hasn't made it even into the overall top 100, which boasts 13 Mario games (including MK), 9 Zelda games and 6 Pokémon games. That's alienating - that the list favors Nintendo games so heavily while your favorites might not have a shot at making it anywhere near the top. In fact, if you compare score averages, Hollow Knight averaged a 14th place among the 5 lists it was in, whereas Mario Kart 8 averaged roughly 20th place; but Hollow Knight is 101st on the overall results, while Mario Kart sits in 7th place. I'm not saying it can't work that way, but it is something to think about.
I think the formula was kept secret in the past, but now that you have revealed it...
Since you are doing a lower score is better format, and any game not showing up on a list gets hit with a 50+10 score, that is doing huge damage to games that only get a few votes. At the same time, it is a bonus to games that get a lot of votes, even if they are low on a list. Do games that get a lot of votes really need a bonus? This is exactly what you are talking about in your last paragraph.
It might take more work, but reversing the scoring and going with the highest score as the winner may work out better. And just a zero score for anything not showing up.
Although I guess you could keep the same format and just hit games not on a list with a 50+1 score. You could take the data from this year and see what happens with that change.
NNID: theRepublic -- Steam ID: theRepublic
Wii U - Currently Gaming Like It's 2014 (Hyrule Warriors) - 11 games in backlog
3DS - Currently Gaming Like It's 2013 (Luigi's Mansion: Dark Moon) - 7 games in backlog
PC - Currently Gaming Like It's 2012 (Borderlands 2) - 11 games in backlog
Mobile - The Simpson's Tapped Out and Yugioh Duel Links