Why is C4 of butynone electrophilic?
Yes, that second resonance structure, the one on the right, is a significant contributor to the overall description of the molecule.  That resonance looks a little different because the p orbitals on the alpha and beta carbons are on $\ce{sp}$ hybridized carbons, rather than the $\ce{sp^2}$ hybridized carbon more commonly seen in enones.   As this second resonance structure explains, alpha-beta unsaturated enones and ynones are both subject to attack by nucleophiles at the electrophilic beta carbon.

Resonance structures, like the one pictured below, explain the reactivity seen in enamines and yneamines (the triple-bond analogue); however, now the positive charge is on the nitrogen and a negative charge on the beta carbon.  Therefore these nitrogen compounds are subject to attack by an electrophile at the nucleophilic beta carbon.