I want to use my game atm for just me and the people who work on it with me, but the only option I see is to take the game off the arcade completely / not making it playable? I would like an option for it to be private if there isn't one already where only people who have an accessible link to the game can actually play it.
The arcade is primarily a showcase for Scirra, so making games invisible to users is of no benefit to them, at a cost of having to host it, bandwidth, etc.
If you want to host your game privately, then you should try a hosting service such as Dropbox, google/microsoft drive etc.