Does the relationship equation between standard cell potential and equilibrium constant violate potential's intensive properties?
No, there is no violation of "intensivity".  The reason is that $K_{eq}$ depends on $n$, and changes in one cancel the other out.

For example, consider the electrolysis of water:


$$\ce{2H2O_{(l)} -&gt; 2H2_{(g)} + O2_{(g)}}$$


The equilibrium constant for this reaction is $K_{1}=\frac{[\ce{H2}]^2 [\ce{O2}]}{1}$ and if you wrote out each electrochemical half reaction separately, $n$ would be 4.

Now consider this reaction:


$$\ce{4H2O_{(l)} -&gt; 4H2_{(g)} + 2O2_{(g)}}$$ 


The equilibrium constant is now $K_{2}=\frac{[\ce{H2}]^4 [\ce{O2}]^2}{1}=(K_1)^2$.  If you wrote out the half-reactions for this reaction, $n$ would be 8, twice as big.  But the $\ln K_{eq}$ term would also be twice as big, since $\ln K_2 = \ln{(K_1)^2} = 2 \ln K_1$.