While ionization of HNO3 does indicate it is an acid, this is not the same as acetylene. I also would not have worded this question in the way indicated. While the hydrogens of acetylene are acidic in the sense that the acidity of the hydrogens of HF, H2O, NH3, and CH4 can also be determined. That is different than determining the equilibrium of acetic, nitric, or sulfuric acid in water. In water, the hydrogens of acetylene are not removed to form acetylide anions and hydronium cations. In that sense, I would not have labeled the acetylene hydrogens as acidic. The net reaction having taken place are the result of replacing the CH hydrogens with a silver atom. The electrons remain with the carbon in that reaction, so a proton was lost in the reaction. In that sense, it is similar to an acid. However, if an alkyl bromide is treated with sodium ethoxide, a proton is also lost in forming an alkene, but we do not describe the alkyl hydrogens as acidic.
What I wished to point out is that the pKa of an alkane is much too high for an alkoxide to remove them in any equilibrium reaction. The bromine atom must in some way alter the pKa of the hydrogens in order for this reaction to take place. I argue this must also be the case for the acetylene hydrogens. If silver nitrate were replaced with sodium nitrate, the product would not be sodium acetylide and nitric acid. Silver is known to complex with alkenes and acetylenes, so it may not be surprising that a complexation may alter the net acidity. I argue it is the complex that enables the acetylene hydrogens to be removed.