I think some people are confusing "Most important" with "most needed to step up." If you consider someone like Gronk a "sure thing" then that means he's probably on this list as him being a sure thing is an important aspect of the offense. Guys like Lloyd and Dowling who the team was a few plays from winning the SB without obviously aren't "most important" as the team was plenty successful without them.
1) Wilfork - the obvious #1. If he doesn't command the attention he gets, the entire front 7 will fall apart and they won't get any pressure. Meanwhile, it's been proven that BB can make the defense respectable as long as he does get great play from Wilfork.
2) Gronk - The most important skill position player on offense. We saw how congested the middle of the field gets in the superbowl when he's not keeping safeties honest shooting up the middle.
3) Welker - Like Gronk and Wilfork, they don't just rely on consistent play from him, they rely on spectacular, mistake free play from him.
4) Mankins - Others won't rank him this high, but with Light and possibly Waters gone, they'll need All-pro play and leadership from Mankins more than ever. Neither Connolly nor Koppen are anchoring the line any time soon, Solder will be in his first year at LT, and Vollmer will be coming off a horrible year. If Mankins has a down year, the line could really struggle.
5) McCourty - imo, McCourty playing well this year is more vital than anyone else in the secondary. They seem to get pummeled with injuries in the secondary every year, and the difference is a corner can fill in at safety a lot easier than the other way around.
6) Arrington - Was the best corner on the team last year and with McCourty needs to provide the secondary with two dependable corners given the lack of talent at safety. Most see him as the full time nickel this year and that's basically a starter in today's NFL.
7) Mayo - Reason he's not higher is, among other things, because they have depth at the position with a guy in Hightower who's capable of calling plays and "quarterbacking" the defense if you will. The main reason he's only #7 is the fact players like him are becoming more useless every year. The key to the defense is gonna be how well it does against the pass which Mayo is never gonna be a huge factor with. Obviously he's on the list because the whole run defense is built around funneling players in his direction knowing he'll make every play he's set up to make.
8) Solder - Don't have him higher because they don't need him to be THAT good right away. Brady can handle some edge pressure if the interior line does its job, they just need him to stay healthy and not be a liability.
9) Chung - Similar reason to Mayo as for why he's not higher...he's never gonna be a great cover safety and the safeties being able to cover better is what's needed. He's on this list because as young as he might be, he's the experienced member of the secondary who'll be needed for leadership and continuity at at least one safety position.
10) Ninkovich - No one else will agree with this, but right now, he's the most proven edge rusher they have. He came alive at the end of the year last year and needs to have an 8 sack season or so since they lost Anderson and Carter. I believe in Cunningham a lot more than anyone else, but neither he nor Jones can be expected to contribute a lot this year.
Unconventional list, but imo, those are the areas they need to show up. McCourty, Chung, and Arrington will all need to stay healthy and gel if the secondary is gonna become the asset it needs to be. Wilfork will be needed to anchor the front 7 and play like an animal with no proven force next to him on the D-line. Ninkovich needs to build on last season and provide a good amount of pressure regardless of what Jones/Cunningham/Fanene/etc. do.
On offense, Mankins and Solder need to basically anchor the line, with Mankins keeping the interior playing well and Solder protecting the edge enough so it doesn't get Brady forcing throws. Meanwhile Welker and Gronk are the two important parts to the passing game staying elite. That's pretty much a no-brainer.
Guys who I think shouldn't be on this list-
Any of the running backs - The fact there isn't a clear cut starter, it's a pass heavy offense that doesn't rely on a running game, and none of them are spectacular means none of them are needed in particular. If both Ridley and Vereen disappoint, then Addai can play a similar role here that he played in Indy as a guy who gets 3-4 YAC while also providing great blocking + catching.
Lloyd - If Gronk, Welker and Hernandez duplicate last year with Gronk's injury at the wrong time withstanding, Lloyd is a mere luxury and added element. As mentioned already, they were a healthy Gronk away from winning the SB without Lloyd. Lloyd might take the offense to an even better level, but it was plenty good without him and w/ a healthy Gronk.
Spikes - He's one-dimensional and that one dimension isn't important in the NFL right now. Hightower is more versatile and imo will start eating into Spikes' snaps pretty quickly. I like Spikes and think he's a good player, but defending the run isn't gonna be the decider for how far they go.