That's the same heater I had in mine. It is indeed installed correctly and the PO (who had owned it for 30-plus years) used the same type of hose that you would find for a dryer exhaust to connect from the firewall to the spot underneath the battery tray. It was kind of a pain in the ass to put that hose up to the grille when it fell off.
Two pictures from when I restored my '67 (hopefully they come out, since they're hosted on Facebook):
Notice the gray tape on the firewall? That's because the PO put in a second heater to help the first! Sadly it was gone by the time I bought it. It was the round one, whose name escapes me.
In this one, you can see where the tube would snake down underneath the battery and connect underneath the left headlight.