The OP's question is:
How can (1) be so acidic even though the two methyls cannot provide any significant stablization?
Answer to that is simple. In Table II of Ref.1 shows in the entries 1-3 that $\mathrm{p}K_\mathrm{a}$ values would effected less by the groups attached to other sidede of the carbonyl groups other than those decreasing the negative charge density of carbonyl carbon such as ethoxy (entry 4) or amino groups or keeping the fixed geometry (entries 5 & 6) of enol once deprotonated. Entry 1 is pent-2,4-dione, which has shown $\mathrm{p}K_\mathrm{a}$ of $13.33 \pm 0.05$. Entry 3 is 1,3-diphynylprop-1,3-dione that has shown $\mathrm{p}K_\mathrm{a}$ of $13.36 \pm 0.06$. The $\mathrm{p}K_\mathrm{a}$s of entries 1 & 3 have shown not much different values even though end methyl groups in entry 1 are replaced by phenyl groups in entry 3, meaning electron withdrawing inductive effect of phenyl ring is overcome by its electron donating mesomeric effect (evidently). However, sigificant increase in $\mathrm{p}K_\mathrm{a}$ has been shown when the change has made to the $\alpha$-carbon of the entry 1. When a methyl group is added to $\alpha$-carbon of the Entry 1, which would become 3-methylpent-2,4-dione, has shown $\mathrm{p}K_\mathrm{a}$ of $15.07 \pm 0.06$ (Entry 2), a 1.74 $\mathrm{p}K_\mathrm{a}$ units increment. Thus, it is safe to say that changes ar reaction center is much more prominently effect the $\mathrm{p}K_\mathrm{a}$ of substrate than changes to any other places.
Followings are some other insights to drastic changes in $\mathrm{p}K_\mathrm{a}$ values of some concerned organic acids. According to the Ref.1, it seems the value of apperent $\mathrm{p}K_\mathrm{a}$ of an organic acid in DMSO is depended in so many conditions such as cation of the base used, its concentration, etc. Eventhough Ref.1 described the condition in details, Ref.2 doesn't even if the principal author in both papers is same. As Ref.1 pointed out the the geometry of the resultant enol plays a role as well.
The Ref.3 provided another dimension affecting $\mathrm{p}K_\mathrm{a}$, which is the steric bulkiness. For example, the effect of bulkiness is evident in the values given in Ref.2. When one hydrogen in each methyl of acetone is changed to methyl group (pent-3-one), the $\mathrm{p}K_\mathrm{a}$ has been changed from 26.5 to 27.1 (0.6 $\mathrm{p}K_\mathrm{a}$ units). The change could be purely electronic and/or mix with steric. But, change of bulkiness is to isopropyl groups (2,4-dimethylpent-3-one) the change of $\mathrm{p}K_\mathrm{a}$ is by 1.7 units, showing clear steric effect.
Then again, When one hydrogen in the methyl of acetophenone is changed to a methyl group (1-phenylprp-1-one), the $\mathrm{p}K_\mathrm{a}$ has actually been decreased from 24.7 to 24.4 (-0.3 $\mathrm{p}K_\mathrm{a}$ units). The change could be purely electronic influenced by presence of phenyl group. However, the change is inceased to an isopropyl group (2-methyl-1-phenylprp-1-one), the $\mathrm{p}K_\mathrm{a}$ is increased by 1.6 units (from 24.7 to 26.3), again showing clear steric effect.
References:
- William N. Olmstead and Frederick G. Bordwell, "Ion-pair association constants in dimethyl sulfoxide," J. Org. Chem. 1980, 45(16), 3299–3305 (DOI: https://doi.org/10.1021/jo01304a033).
- Frederick G. Bordwell and John A. Harrelson, Jr., "Acidities and homolytic bond dissociation energies of the $\alpha \ \ce{C-H}$ bonds in ketones in DMSO," Can. J. Chem. 1990, 68(10), 1714–1718 (DOI: https://doi.org/10.1139/v90-266).
- Michelle H. Dunn, Nicholas Konstandaras, Marcus L. Cole, and Jason B. Harper, "Targeted and Systematic Approach to the Study of $\mathrm{p}K_\mathrm{a}$ Values of Imidazolium Salts in Dimethyl Sulfoxide," J. Org. Chem. 2017, 82(14), 7324–7331 (DOI: https://doi.org/10.1021/acs.joc.7b00716).
