The only constraint is for right turns. If you plan to turn right, you should follow the procedure, especially if it's IFR. If you plan to fly straight ahead or turn left, you meet the minima for a safe departure using standard climb rates.
There is NO REQUIREMENT to make a right turn.
Takeoff minima procedures do not take adjacent ATC airspace into account, however. It's up to the pilot to know that the airspace is there.
Looking at the sectional, there's a ridge to the west of the airport that starts at 1000 feet (400 feet above the field), and gets higher to the southwest. That's the reason for the restriction.
Some charted procedures will have "avoid such-and-such airspace" on them, but these are usually found only on published IFR departure procedures (and approach plates), such as the LLADN1 at Hulett, Wyoming. Note the instructions for Devil's Tower and the Powder River MOA.