The H-Bridge%20relay.pdf circuit uses reed relays. They are neat because their coils can be energised with low current. The flip-side to that feature is that their contacts are not capable of switching large currents, < 1/2A.
To energise relays with bigger coils, and bigger contacts, you’ll need a transistor.
You could run your motor with the reed relays, if you want to do some experimenting, but once the motor starts to do some work then it will probably roast (weld) the contacts of a reed relay.
The switching logic is still the same.
Kendall didn’t make a very good schematic. I re-worked it a bit and have attached it. (If you’re running the 12V motor, apply the +12V at the points labelled “+5”.)