As bart said, you monitor can already stream 720p. However, to do that you have to either
* Play the game in a 720p window in the middle of your screen in Windowed mode, or
* Play the the game taking up the full screen, but fill in the black bars with other content in OBS
The question here isn't whether you can stream in HD, it's whether you can stream in a 16:9 resolution and have it not have black bars. You can either change your game to be a 16:9 resolution (option A above), or embrace the black bars and fill them with extra content (such as stream chat, webcam, slide show, or something else).
Or you can just live with a 5:4 stream.