Is intervention necessary to prevent siblings who are disobedient from acquiring and operating forbidden things (such as video films and songs, magic films, and PlayStation games), or is it sufficient to offer advice while leaving them to do as they please and bear their own sin?

You have done well in advising your siblings and forbidding them from unlawful acts, and this is your duty. Continue to do good and call to it, and pray for their well-being and steadfastness. Gentleness, wisdom, and good counsel are the path of دعوتك (your call/invitation). Your patience with their harm increases your reward, and Allah will assist you and guide others through you.