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Thanks for asking Josh!
Right now, Remote Buddy only works to control whole apps. It's not currently capable of detecting the content of your browser window and send site-specific key presses.
If you want to only control one site, however, you can go to Prefs > Mapping > Safari and adjust the actions assigned to the button to send the key presses you need to control that particular site.
If those keypresses are just arrow buttons, space bar and return key, you can just use the respective actions from the Virtual Keyboard. Otherwise, you may need to use "Custom actions…" to create actions to send different key presses.