StreamerKit is an overlay application, which requires the VR runtime to have an Overlay feature, which Oculus mode does not. In order to run the game in openvr mode, the game needs to be purchased from Steam or somewhere that is not the Oculus store, and then you need to modify the launch option.
If you acquired the game from a different store than Steam you'll want to do the equivalent launch options to run the game. If your store platform does not have a launch option create a shortcut to the game executable and add the launch option there.
1: Make sure that your monitor is plugged into your GPU and not your motherboard graphics port.
2: Go to Properties on the game under the library and then find the Launch Options
3: Set a launch option of -vrmode openvr if it is a Unity game, or -hmd=SteamVR if it is an Unreal engine game. Use these launch options in the target of a shortcut if necessary.
(I have an Oculus headset and LIV isn't capturing my game; I can't see the chat box or alerts in my headset)
4: Go to SteamVR -> Settings -> Developer and make sure where it says Current OpenXR Runtime it is set to SteamVR. If it is not click the button below that says Set SteamVR as OpenXR Runtime.
5: If neither of these work or make the game not have controllers you can try setting the game executable to run in Windows 7 Compatibility Mode. To do this go to the location of the games executable, right click the executable and then click on properties, go to the compatibility tab and then select the compatibility mode. Note this method can sometimes have undesirable side effects like not having any controllers or other things not functioning.
6: Try launching it from the Steam desktop app and select "Launch <Game> in Steam VR Mode"
7: If you use an Oculus Quest you should try Virtual Desktop (purchased from the Quest store) instead of Oculus Link as that makes the Quest act more like a native SteamVR headset and can get the game to run in OpenVR mode. Use this in combination with the vrdesktop.net desktop streamer app inside of steamVR.
8: If none of these work you will need to contact the game developer about allowing you to run their game in OpenVR mode for Oculus.