If you're using OBS or Streamlabs to record your PNGtuber and game footage, you would just adjust filters and layering in there to ensure your character is properly captured. You would have 2 Game capture layers - one for VeadoTube and the other for your game - arranged as you see fit. Add a filter to VeadoTube set to "Chroma Key" in order to turn the green from the interface transparent.
Being able to see VeadoTube while you're playing a game - regardless if the capture picks it up - depends on the other game's settings (like maybe switching to non-fullscreen mode and shortening the game's display dimensions).