No you don't have to restart all over, you can interpret the theme any way you like, it can be a small part of the game or a core part of the game. Just know, theme is one of the voting categories.
My first game jam, I finished my game, submitted it, and was halfway through the voting period before I realized my game followed the theme "Reverse" and not the actual theme "Rewind" :)
I still got a lot of great feedback from people and learned a lot in the process.
The theme is just a guide to get the creative process started.
