Based on the papers I've found, the answer is correct.
According to Bouchoux,[1] ethynylbenzene – an analogue to the compound in question – the $\Delta G$ of deprotonation for terminal $\ce{H}$ of ethyne group is $\pu{1522.2 kJ mol-1}$ while that for ring $\ce{H}$s of benzene at o-, m-, p-positions are $1612, 1614,$ and $\pu{1614.1 kJ mol-1}$, respectively.
According to Koppel,[2] $\Delta G$ of methyl $\ce{H}$ for toluene is $\pu{373.7 kcal mol-1}$ (equivalent to $\pu{1564.23 kJ mol-1}$).
According to Hansch,[3] the Hammett constant for methyl substitution is $-0.07$ and $-0.17$ when it is at m- and p-position, respectively, which means that being substituted by a methyl of phenyl ring would almost not affect its proton acidity.
So, the sequence is ethyne's $\ce{H} \gt$ methyl's $\ce{H} \gt$ benzene ring's $\ce{H}$.
References:
- Bouchoux, G. Gas phase acidity of substituted benzenes. Chem. Phys. Lett. 2011, 506, 167-174. DOI 10.1016/j.cplett.2011.03.032
- Koppel, I. A.; Koppel, J.; Pihl, V.; Leito, I.; Mishima, M.; Vlasov, V. M; Yagupolskiid, L. M.; Taft, R. W. Comparison of Brønsted acidities of neutral CH acids in gas phase and dimethyl sulfoxide. J. Chem. Soc., Perkin Trans. 2 2000, 6, 1125-1133. DOI: 10.1039/B001792M
- Hansch, C.; Leo, A.; Taft, R. W. A survey of Hammett substituent constants and resonance and field parameters. Chem. Rev. 1991, 91, 165-195. DOI 10.1021/cr00002a004