Short answer: not necessarily.
The Video Management exclusive license will not affect your agreement with YouTube. The reason being is that we claim your video in YouTube on your behalf just so we can post it to our own channels. As it stands under YouTube's policy, only one account can manage a video at a time, so for us to be able to post it to our channels we need to claim your vide. Keep in mind the video remains in your channel, but we will try to maximize its reach by posting it in other channels as well. One of the benefits of this license is that we have Content ID access, so we're able to represent you and take down unauthorized/stolen copies of your videos made by other Youtube users.
Alternatively you may continue managing your YouTube videos independently of Rumble, to do this simply select Video Management (excluding YouTube). This way the videos you post to rumble will be shared in our site and our Third party partners only, but we will not post a copy to our YouTube channels, nor will we be able to claim stolen copies made by other Youtube users if they exist.