Why does treatment of a geminal dihalide with sodium amide lead to an alkyne and not an allene?
Sodamide is bloody dangerous.  If your bottle is too old, it likely has begun to oxidize some and you have potential azides or other polynitrogen compounds that may lead to an explosion.

Even with good stuff, generally the reagent is not heated to avoid similar complications.  This means normally this reagent works at low temperatures (often times dry ice/acetone).  Under these conditions kinetic products are favored over thermodynamic ones.

The exomethyl group is much more accessible for deprotonation, and so kinetically, I would expect the amide ion to abstract the terminal hydrogen.



After that, the resulting bromoalkene still has the possibility of forming the allene product, but the transition state resulting in elimination to the alkyne is favoured as the vinylic hydrogen and the bromine are always locked in an anti conformation due to alkene geometry, as indicated in the above diagram. On the other hand, the allylic hydrogen may not necessarily be anti to the bromine due to C–C bond rotation.