Weirdly enough the procedure posted by the OP is not applicable to -700IGW and 800 with PATS Auxiliary Fuel Tanks as that is not a boeing configuration.
Anyway, just checked and our DDPG says:
For -300/-400/-500/-600/-700/-800:
1. When dispatching with one operating pack supplied by engine bleed air on
takeoff:
A. Determine V1(MCG) based on engine bleed for packs OFF.
B. Determine takeoff performance based on packs AUTO.
2. Limit altitude to FL 250.
3. ER operations are not allowed.
4. For galley 4B food cart chiller installed, use only one chiller inflight.
5. Position the associated PACK switch to OFF.
6. Position the ISOLATION VALVE switch to CLOSE.
7. For increased air flow when the flaps are extended (takeoff and landing), use the APU to supply bleed air to the operating pack.
A. Right pack inoperative
1) Do the Supplementary Procedure - Air Systems “No Engine Bleed Takeoff and Landing” (Refer to the Flight Crew Operations Manual).
NOTE: Keep the PACK switch to OFF and the VALVE switch to CLOSE.
B. Left pack inoperative - PRIOR to takeoff or landing
1) Engine No. 1 BLEED air switch to OFF
2) R PACK switch to AUTO
3) L PACK switch to OFF
4) ISOLATION VALVE switch to OPEN
5) Engine No. 2 BLEED air switch to OFF
6) APU BLEED air switch to ON.
C. Left pack inoperative - AFTER takeoff or landing
1) APU BLEED air switch to OFF
2) Engine No. 2 BLEED air switch to ON
3) ISOLATION VALVE switch to CLOSE
4) Engine No. 1 BLEED air switch to ON.
The MEL simply states that only one pack is required with a restriction to max FL250 and no ER operation allowed, without any direction to consult the DDPG as is usual if there is a procedure to be followed.