Although Ben Norris has given excellent explanation for why the steric hindrence is not playing the role in the reaction of cyclohexanone with excess methyl iodide to give tetramethylated cyclohexanone, there is an enother reason why reaction proceds so smoothly under given condition to give more than 80% yield of 2,2,6,6-tetramethylcyclohexanone. It is the exceptionally high reactivity of $\ce{KH}$ towards ketones compared to that of other strong non-nucleophilic bases such as $\ce{NaNH2}$, and even $\ce{NaH}$ and $\ce{LiH}$ (Ref.1):

As shown in the graph above, methyl tert-butyl ketone (pinacolone) has given 100% metallated enolate within $\pu{5 min}$ in the presence of $\ce{KH}$ at $\pu{20 ^\circ C}$ while it has taken more than $\pu{120 min}$ to give at least 20% metallated enolate with $\ce{NaH}$ under same conditions. For comparition, $\ce{LiH}$ is even less reactive than $\ce{NaH}$ (Ref.1). In a typical reaction ($\pu{25 mmol}$ substrate in $\pu{40 mL}$ of THF in the presence of $\pu{28 mmol}$ of $\ce{KH}$), cyclohexanone is enolated 100% within $\pu{1.5 min}$ and 2-methylcyclohexanone is enolated 100% within $\pu{6 min}$. In the latter case, which can give two enolates, the ratio of isolated enols (as silyl ethers) was found to be $33:67$ less substitured one to more substituted one indicating that reaction is more facile with making more stable enolate even in the presence of steric hindrence.
Thus, it is clear that the question in OP's post is directly related to the reserch done in Ref.2 (which is mentioned by Waylander in his answer. Accordingly, the authors in Ref.2 reported yield of 2,2,6,6-tetramethylcyclohexanone as 96% (GLC analysis) and as 81% (isolated yield by distillation), which is the exact yield given in the question. The procedure was as follows:
To a flask containing $\pu{216 mmol}$ of $\ce{KH}$ in mineral oil $(\pu{40 mL})$, which is in a waterbath maintained at $\pu{25 ^\circ C}$, $\pu{220 mL}$ of THF was added first and then $\pu{5.2 mL}$ of cyclohexanone $(\pu{50 mmol})$ was added dropwise over a $\pu{5 min}$ period. The mixture was stirred for additional $\pu{5 min}$ and $\pu{13.5 mL}$ of $\ce{CH3I}$ $(\pu{216 mmol})$ was added dropwise over a $\pu{15 min}$ period. The reaction mixture was stirred for additional $\pu{15 min}$ before workup with water. The simple distillation of dried organic layer gave $\pu{6.25 g}$ of expected product (81% yield).
References:
- Charles Allan Brown, "Saline hydrides and superbases in organic reactions. III. Facile reaction of potassium hydride with ketones. Rapid, quantitative formation of potassium enolates from ketones via kaliation," J. Org. Chem. 1974, 39(9), 1324–1325 (DOI: https://doi.org/10.1021/jo00923a042).
- Alan A. Millard and Michael W. Rathke, "Procedure for the permethylation of ketones using potassium hydride and methyl iodide," J. Org. Chem. 1978, 43(9), 1834–1835 (DOI: https://doi.org/10.1021/jo00403a055).