Link Hogthrob's infobox says "Steve Whitmire (2000-2016)". However, as far as I can tell, Link's only appearances that year were a background cameo in the TV series, and the web videos, which were filmed in 2015. So shouldn't it say "Steve Whitmire (2000-2015)"? Or am I forgetting something?
We count the year the thing came out.
Well, for the most part we do. The real exception being when there's a hard/definitive stop to a performer's tenure (such as death). For example, Ol' Brown Ears is Back came out in 1993, but we list Jim Henson as performing Rowlf from "1962 to 1990" (ending when Jim died, not when Jim's last work as Rowlf came out). Likewise we've ended Kevin Clash's tenure as Elmo in 2012 (based on his November 2012 resignation from Sesame Workshop) despite Kevin-as-Elmo material continuing to come out in the 2013-14 season of the show.
Steve was still the go-to performer for Link up until his dismissal in October 2016 (regardless of whether he had put his hand in the physical puppet that year or not). There was Link content released in 2016 with Steve performing so I think it's fair to still list 2016 as his end date and not get too pedantic or speculative over when that material was produced.
Right, there are exceptions. We wouldn't say Jim Henson performed Rowlf until 1993 just as we wouldn't say he performed Kermit until 2014 because an archival recording of his voice was used in Muppets Most Wanted.