For my own personal list, I consider ports, expansions/DLC and remakes. With the caveat being that the port is of a game that's still relatively new (i.e. released in the previous year or two). For example, I included Hollow Knight on my 2018 list despite it releasing on PC in 2017. Because it was the first release for consoles, for me that's "new enough" to qualify IMO. Beyond that, expansions and remakes can be substantial, original content that can certainly go toe-to-toe with wholly new full game releases.
But that's just how I prefer to do it. As far as this site goes, I don't have a problem with anything being eligible as long as it had a release that year. If someone feels strongly that an unfinished episodic series or early access game is one of the best things they've played that year, then by all means they should be able to vote for it.
Remasters is the only category I'm a bit iffy on. It kinda goes back to how I'd draw a line with respect to whether or not a port is "new enough", because in both cases we're talking about a re-release of what's essentially the same content (except Batman on the Wii U, naturally -- that was for you, Reggie!). I would probably count ports/remasters of anything that initially released in the current generation, but nothing older than that. But I also wouldn't get up in arms if people felt strongly about remasters/collections featuring old games.
If I were part of a website/publication or putting on an awards show like Geoff does, I would limit the eligibility a bit more. I think in that situation, I would only want to be voting for fully released software that came out that year. So from the poll, I would only include remakes and expansions/DLC. Games like RE2 and the forthcoming FFVII remake should count as they are very different from the original source material, and in the case of DLC stuff like Minerva's Den and the Witcher 3 expansions are substantial and strong enough to stand on their own.
For episodic games like Life is Strange, I would have them be eligible in the year that the final episode is released. It's less that I think it "shouldn't be allowed", and more that I wouldn't feel comfortable judging it without experiencing it in its entirety, or voting for the same game in consecutive years. I think even in the case of something like Hitman S1, if only half of the episodes came out in 2016, I wouldn't consider it to be eligible until the next year (even if you could make a very compelling argument that individual maps -- i.e. Sapienza -- were good enough to be in the running on their own).