While vacuum tubes are much more consistent than other discrete active devices such as transistors, MOSFETs, and FETs, if you want tight tolerances, then look to passive devices, as 0.01% tolerances only exist in passive components such as resistors and capacitors.
Still, why so large a difference? Part of the answer is found in the formula's assumption of a perfect triode. Another part is found in the tube manual's imprecision in stating the mu and the rp of the 6SN7 which, in this case, forms the larger part of the error. A careful inspection of the plate curves reveals that at 250 volts and 9 mA, the mu is closer to 21 and the rp is closer to 8k or 9k. If we recalculate the cathode resistor's value using these revised values, then much of the difference disappears between formula and plate curves.
Aren't a triode's mu and rp fixed and immutable? No. Unlike a tube's dimensions and mass, its rp, mu, and Gm vary, depending on plate voltage and plate current. The least varying characteristic is its mu; which is ironic, as it is the least real of the three specifiers, defining only the relation between rp and Gm, not any actual physical aspect of the triode's design. (Naming the ratio between a man's height and the circumference of his waist "phi" might be useful for predicting heart attacks, but phi is not real in the same way that his eyes or kidneys are real.)
Often, most of the blame for inaccurate results lies with the difference in cathode-to-plate voltage that the tube manual specifies versus the voltage the formula assumes. The tube manual assumes that fixed bias will be used, thus retaining the full B+ across the tube, whereas the formula accounts for the voltage lost across the cathode resistor.