Currently (as of June 2019), there is no option in the new YouTube Studio (still in Beta) to batch delete multiple videos at once. You have to click the Options button (three vertical dots) next to each video and select Delete.
The only workaround I found is to switch back to the old Creator Studio. To do that simply click Creator Studio Classic button in the bottom left of your screen.
Once back in the old Creator Studio, select all videos you want to delete, then click Actions > Delete
June 2019
YouTube Studio Beta
YouTube Creator Studio Classic
