For me, it's like shooting a shotgun. I use my bow hand to "point" or "swing" on the target. Yes, you need to focus on the smallest spot you can and track that with your bow hand. One problem I see with many shooters though is that they tend to rush the shot and don't get their full draw alignment. This is especially true if you are the one throwing or motivating the target. By "rushing, I don't mean not shooting fast but the shooter still must compete the draw and release like they are used too. There's more time available than many think.
Another error many make is that they stop the bow hand movement when the shot is released. This is a common cause of a miss with a shotgun too. The bow hand must continue to track the moving target all the way to arrow impact. As Bob Wesley told me " Line, rhythm and follow through!" Allow or make your bow hand continue to track and point at the target after the shot. Just like the old static target advice, keep the bow hand on target until arrow gets there.
Moving targets are a lot of fun and even more fun when hitting them.
Arne