The reason I say this is a capitalist endeavor is the recognition of an asset (the daughter), the want to see the most return (as large of a bride price as possible), and then seeking to improve the asset through education, travel, and competition to lead to a better selling price.
By default in communist regimes women are by default the regime's means of prosuction, destined to a life of work while kept on a maintenance plan by their masters. So whether they aren't being sold, they are managed like an asset, where low upkeep abd high output is favoured while high maintenance and problematic/opinionated individuals are destined to be written-off sue to their impact on production.
Turkmenistan's recent history is as a (Soviet) socialist republic and it ranks very, very low on https://en.wikipedia.org/wiki/Index_of_Economic_Freedom. I'd need further convincing that this practice is reflective of a culture which embraces capitalistic ideals like free markets and voluntary exchange.
That a transactional system exists in a dictatorial regime that bears some communistic characteristics doesn't mean that transactional system (bride price) isn't "Capitalist".
Ah, the classical "no true scotsman" that pops up in every discussion on the virtues of communism.
It's weird how people praising or arguing in favour of communism repeatedly claim that communism never existed, particularly unsavoury and atrocious communist regimes, but somehow every single far-fetched example involving some kind of transaction that has a negative connotation is somehow a prime candidate to represent capitalism.