In a protocluster USS1558-003 at z = 2.53, galaxies in the dense cores show systematically elevated star-forming activity compared to those in less dense regions. To understand its origin, we look into the gas properties of the galaxies in the dense cores by conducting deep 1.1 mm observations with the Atacama Large Millimeter/submillimeter Array. We detect interstellar dust continuum emission from 12 member galaxies and estimate their molecular gas masses. Comparing these gas masses with our previous measurements from the CO(3-2) line, we infer that the latter might be overestimated. We find that the gas to stellar mass ratios of the galaxies in the dense cores tend to be higher (at M ∗ ∼ 1010 M o˙ where we see the enhanced star-forming activity), suggesting that such large gas masses can sustain their high star-forming activity. However, if we compare the gas properties of these protocluster galaxies with the gas scaling relations constructed for field galaxies at a similar cosmic epoch, we find no significant environmental difference at the same stellar mass and star formation rate. Although both gas mass ratios and star-forming activity are enhanced in the majority of member galaxies, they appear to follow the same scaling relation as field galaxies. Our results are consistent with the scenario in which the cold gas is efficiently supplied to protocluster cores and to galaxies therein along surrounding filamentary structures, which leads to the high gas mass fractions and thus the elevated star formation activity, but without changing the star formation law.