I agree that the rent sounds high. Is anyone else interested? How bad do they want (and need) to lease this space? Negotiate hard for a lower lease for your benefit. Get it down as low as you think they will go, and make sure they know you are not afraid to walk away if the price is not right for you. It is great to have those free months in the beginning to help you get started, but make sure you can still pay yourself something once the full rent kicks in.
Also, I would recommend researching the gaming industry to make sure the game room is attractive enough to draw the young gamers away from their already paid for big screen HDTV, comfy chairs, and free refreshments in the kitchen that they have at home. From my observations, many arcades that only have games are being closed. The more successful gaming businesses I know of offer go-carts, mini-golf, food, and other attractions in addition to games. It would take the right combination to convince people to leave their Wii, Xbox, or Playstation at home to go to a place where they have to pay to play. Getting the correct set-up could be expensive in the beginning and you would have to make a really good first impression.
I am not saying the idea is not good. I am just offering up my thoughts. I am sure you have considered many issues surrounding the situation and know more about it than I do. Basically, my advice is to figure out how to sell the EXPERIENCE of your movie and gaming business. You have got to draw people in based on something other than a few arcade games and some video consoles hooked to a TV.
As far as the dedicated theaters, I would make sure you knew what your customers want and play to their wishes. You may not need to dedicate screens full-time to different genres, but mix-and-match based on what you can select from.
Keep us posted and I wish you the best!