To me, this is a damn symbolic scene. Raghu succeed to find Dr. Kaul's ring first!! He won the game where the winner is supposed to win over Antara's heart. Isn't it indicating that Raghu is going to get her forgiveness after he will do something HUGE about Dr. Kaul's memory or his family??
His getting that ring as gift indicates that someday he will be a part of Dr. Kaul's everything!! He will be the reflection of Dr. Kaul to Antara.
Antara's making him wear that ring may indicate the future when Antara herself will help him to get out of his guilt. She will forgive him ultimately.
I am hopeful now.