What is the ruling on listening to music coming from the television operated by parents who are hard of hearing, and is it permissible to eat with them and play Scrabble in this situation, and what does the use of earplugs change in the ruling?

You must be dutiful and kind to your parents, and sit with them during times when they are not playing music. Advise them gently and kindly regarding the impermissibility of music. Do not sit with them where reprehensible acts are displayed, for Allah the Almighty says: "And He has already sent down to you in the Book that when you hear the verses of Allah being denied and ridiculed, then do not sit with them until they enter into another conversation. Indeed, if you did, you would then be like them." (An-Nisa: 140).

As for the sound reaching your room, you are not sinful for it. What is forbidden is intentionally listening to music, not merely hearing it unintentionally or without paying attention, as narrated from Ibn al-Qayyim and Ibn Hajar al-Haytami.

If there is a need for you to sit with them, and they do not refrain from the reprehensible act after your advice, there is no sin upon you if you avoid intentionally listening.