Currently, Smartsheet does not support the drag and drop feature for Card View on a touch screen.
I have a ProLite T2736MSC touch screen monitor and I would like my team to be able to physically drag and drop my Smartsheet cards by touching the screen. This is a feature which is possible on Android/IOS and probably not difficult to implement on monitors as well. Cards can be opened by touch to view information in them, however the ability to move these cards to different columns by drag and drop is missing.
FYI, I have seen several online forum posts about this issue from other Smartsheet users.