What do you mean by an 'indoor' vine? Some species of vine, like the typical Black Hamburg, will ripen better if they are under cover, but then it's always recommended that the roots are planted outside.
If this is just a grape vine in a container, I expect being restricted has made it produce some fruit this year. If it's a small plant in a relatively small pot, then you will run less risk of weakening the plant by removing most of the bunches, but I'd still keep a couple to ripen on the plant and harvest.
While you CAN grow vines in large pots and containers, they will always do better with their roots in the ground, and in a pot you need to water and feed them very regularly.