Yes, this is another example of the legal system's nasty habit of torturing plain English well beyond its meaning.
Execution, per se, is neither cruel nor unusual. Especially in the context of the time when the Constitution was drafted, a quick, humane execution is the very antithesis of "cruel and unusual".
The truly cruel punishments of the 18th century are the type to make any person cringe and sicken at the thought. Prisoners were quite literally tortured to death in the most horrific and painful ways imaginable. We do not and HAVE not punished criminals in "cruel and unusual" ways in the US.
The "remove all accountability" culture which has grown up in the world just can't grasp the principle behind capital punishment. Some crimes are so horrible that the perpetrator's life should be forfeit. Aggravated kidnapping of a child from her own bed, with repeated aggravated rape is ABSOLUTELY in that category.
Not as part of the legal system, not since we became a separate nation.
People were tortured to death in the old colonial days. And during lynchings as recently as the last century.