So here is a follow up by euro gamer with some new info on the upcoming exclusive strikes being released in September.
http://www.eurogamer.net/articles/2015-06-24-destiny-extra-content-for-all-platforms-when-sony-timed-exclusives-launch-on-xbox
The article doesn't clarify but I feel pretty safe assuming that they will be counting this new taken reskinning of the undying mind as a "new" strike.
My evidence just look at bungies history so far. They even seem proud of recycling content into a "new" experience. On top of that the new hunter subclass has a short cutscene where you clearly find the void bow on the body of a guardian in the black garden.
My prediction is this will be considered one of the "new" strikes and how the new hunter subclass is unlocked. Personally I'm glad for the fresh look at it if it doesn't count as a new one but I'm very skeptical. It's also strange that they would repurpose a strike that is already a partially repurposed story mission. Seems like hopefully unintentional rubbing salt in the wound of those resenting the lack of novel content.
Edit: I'm leaning more towards the subclasses probably have missions and they shouldn't count this, the flayers, or Cerberus as new.....but I still can't help but be skeptical with bungie. I don't think I'll ever be able to expect better again. Hopefully this means I'll be pleasantly surprised