I think you are mixing two things here,
VirtualPriting using ThinPrint components, this is the time when we don't have to install any print driver in Remote Desktop, but the Horizon Client device based print drivers will do the job for you.
'Because print jobs are sent directly from the View desktop to the printer, the HP printer driver must be installed on the desktop.'
While if you are using Location Based printing, in that case you got to install particular make+model printer device driver in the 'Remote Desktop', because it has nothing to do with those thin print components. In that case definitely print job is initiated directly from that remote desktop.