Not trying to state the obvious, but Keyless entry is used so you dont have to use a key to open the doors. Honda factory alarms are fairly simple to integrate into with the keyless entry so when you lock and unlock the doors via remote, the factory alarm arms and disarms correspondingly. The unit you have photographed does not offer that feature as you can see by the basic wiring configuration. If I had to guess, I would say that looks like a inexpensive unit from either JC whitney or maybe Pepboys. You do not want to waste any more time looking for a remote for that unit, its not worth it. Get a new system from a reputable car audio retailer in your area.
On a side note, the factory NSX alarm is very basic and really provides only minimal protection as compared to an aftermarket alarm. And any good alarm will come with keyless entry as a standard option. If you are looking to protect your car, an aftermarket alarm is the way to go. Try a Compustar or Viper. They are two of the more reputable companies.