Gore vs. Rivers: I disagree with the comparison. And, yes, that is a bit of my fandom speaking. But that aside, I think if you make top 3 all time in the primary thing your position is designed to accomplish (in Gore's case, pick up yards on the ground), I think that puts you in, pretty much regardless of anything else.
Eli vs. Rivers: I don't think either should get in. But Eli getting in shouldn't really impact whether Rivers gets in either. I'm going to speak out of both sides of my mouth for a minute here, but...while I don't think "winning the big one" should be the be-all stat, it does count for something. And while I don't think Eli is HOF material, if others feel he is close, and that the wins push him over the top, I cannot overly disagree. They do count for something, especially for a guy who, despite his shortcomings, was the leader of his team for those two wins, and who had to battle for those wins (it wasn't a case where the talent in their conference was severely lacking and they had a cakewalk through the playoffs the years they won it).
In any case, while I don't have strong feelings one way or the other (I don't have strong feelings about the HOF in general), my opinion is that Rivers doesn't quite make the cut, despite having a great career and being a great leader on his teams.
*Edit: I'll also chime in to back TAC and King on Edelman being more than what we typically refer to as a "role player." I agree with the general sentiment that he is not HOF material, but his contribution being sold short by relegating him to "role player" status. I mean, I get that maybe he "technically" fits that description. But when I think of that description, it generally isn't used to describe someone who has a sustained role as one of a team's key players.