Not all markets are based around exchange. Kidney exchange markets, for instance, have a component based on a donor giving a kidney for nothing in exchange, starting a chain of kidney donations that could otherwise not occur.
Matching markets are another example that is not based around exchange
It can be traced back to hunter-gatherer populations honestly. So what?
Mutual aid is pretty far away from abolishing the state or abolishing the private ownership of the means of production, which were the bigger ideas of Bakunin and Kropotkin.
I don't think it's possible to view this as a free market solution unless you want the term "free market" to lose all meaning. The free market does not have a monopoly on rational decision making. Any market is based around exchange, which this project expressedly rejects.