Mackey was already waived. If the Rangers are worried about losing Robertson to waivers, they may send Mancini down since he is exempt, rather than risk losing Ruhwedel. Ruhwedel isn't great, but he provides experienced depth.
Berard, Edstrom and Rempe are all waiver exempt. Any of them could be sent down to begin the season, though I expect the first will be Berard. I'm guessing the only reason he's still with the team is because of Panarin's injury.
Sending down Berard and Mancini gets us to 14 forwards and 8 dmen. The last cut will depend on Lindgren. If he is ready for opening night, I would expect one of Robertson or Ruhwedel to be waived (whichever they feel is less likely to be claimed). If Lindgren isn't ready, I would expect one of Edstrom or Rempe to be sent down.
If Mancini and one of Edstrom/Rempe get sent down, I know a lot of people will lose their minds, but them being waiver exempt is going to work against them. Drury is going to use that to ensure we don't lose any of our limited depth. All of those players will likely play a significant number of NHL games this season, regardless.
It's possible that Vesey is placed on LTIR and we carry an extra player to fill that spot, but then we won't be accruing any cap space to start the season.
In what way has Robertson shown that he is ready? Not being worse than Ruhwedel isn't an accomplishment. The only thing that may keep him on the roster is his waiver status.