这个和need有点像,need doing 是以“物”作为主语,比如My car need repairing.车该修一下了.
同理,want doing也是以物为主语,区别于sb.want to do 以人为主语；
而want to be doing很明显强调be doing,即“想要做某事（持续性的）”,这个通常以人作主语,如
I want to be walking around the park.
Hope these will help.^