Is it permissible to perform the Tarawih prayer individually at home while listening to the recitation of the Imam of the Grand Mosque (Masjid al-Haram) from the television, without seeing the image, and without the intention of following him as an Imam of a congregation?

Your prayer is not valid, because listening to the Imam's recitation via television does not substitute for your own recitation. It has been authentically reported from the Prophet, peace and blessings be upon him, that he said: "There is no prayer for one who does not recite the Opening of the Book (Surah Al-Fatihah)." And if you listen to the recitation of the Imam of the Haram and then recite for yourself, this contradicts your devotion and concentration in prayer.