No. Keep your eyes open during the training blocks for the treatment to be effective. The brainwave frequency being trained is part of your visual system and responds to the games you are playing. When you close your eyes, the training shifts to a different brain area that is not linked to chronic pain.
Neurofeedback uses visual and audio feedback, so you need to train with your eyes open to get the full benefit. In the first few weeks, you may feel tired during training, which is normal because your brain activity is changing. If you feel tired during a session, you can close your eyes during the rest break, and when you feel ready, continue with the next training block with your eyes open.