Allow 720p videos on YouTube app
Your screen resolution being 960*540 is not meant to play 720p videos  because the resolution is lower. That's why the Youtube app detects the device resolution and does not show higher video qualities. The maximum video quality that the Youtube app will show for your device is 480p.
720p = 1280*720

However, you could use YouTube Vanced. It is a modded version that offers more features than the official Youtube app such as:


Override Maximal Resolution

Preferred Speed and Resolution



For rooted phones, L Tweaks, an Xposed module, allows to set video qualities up to 4320p.