Part of the reason that buybacks are referred to as shareholder payouts, is the common context of such buybacks happening after government subsidies. See here an article discussing this occurrence: https://financialpost.com/investing/share-buyback-binge-on-hold-as-companies-line-up-for-covid-19-relief
In short, one method of supporting the economy through hard times, is for a government to provide funds to businesses [other common alternatives would be providing direct taxpayer relief, or increasing funding to government projects, etc]. The general theory behind this is that if the market is competitive, then perhaps jobs are best provided by independent businesses. Therefore, to keep the unemployment rate low while avoiding 'government inefficiency', businesses are provided funds [perhaps grants, perhaps low-interest loans] that in theory allow them to stay open, thus avoiding layoffs and maintaining steady paycheques.
The problem with share buybacks, is that if a business receives a government grant, that is only economically 'efficient' [even in theory, which I will not get into here] if that business reinvests it in its operations [building new locations, hiring new workforce, investing in operations, etc.]. Without the government grant in the first place, the argument is that the business itself would have lost value, so buying back shares at its old value is basically a government grant that ends up in the hands of shareholders [whether they accepted the buyback offer or not], rather than in the pockets of employees.
In that context, this is a payout to shareholders at the expense of government.