Why do death-penalty states have such high murder rates compared to non-death-penalty states?

This is just a guess, but the states with death penalty statutes also tend to have fairly relaxed gun laws. 

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The problem is that your statistics are in error, because they fail to account for standard deviation, and fail to account for statistical error. This is because it only accounts for "discovered" homicides in which a guilty verdict was returned.Thus, it doesn't show the true rates.

Research has shown that the death penalty is not an effective deterrent to crime...

"There are lies, DAMNED lies, and STATISTICS." (Mark Twain)

There's other factors involved because it isn't a direct relationship. Even if there is a death penalty available, it doesn't mean anyone is executed in the past 5 years. The average time on death row is a long time, and we know it doesn't deter crime in how it is applied. 

The closest ties to homicide are income inequality, lack of respect among people. Death penalty illegal shown as *

top 10 homicide rate 2018 6.9/100,000 population or higher

Louisiana, Missouri, Alaska*, Maryland*, N Mexico*, Alabama, S Carolina, Tennessee, Arkansas, Illinois*

Bottom 11 at 2.0/100,000 or less

S Dakota, N Hampshire*, R I*, Vermont*, Iowa*, Maine*, MN*, Utah, Idaho, Mass.*, Oregon

Wealth inequality in at the center or root cause of many issues in the USA, but it is difficult to measure by US State. It probably isn't by US State boundaries either and could be linked to particular cities. There is no easy link of cause of homicide or we could solve it.

Fewer minorities.    

They are red states, that is all you need to know.