AFAIK it's not a solution, it's just a workaround.
As others have said, the previous workaround was a cron event that would invoke a function every few minutes to keep it warm. This is a lot better than that.
They're still working to get cold starts as fast as possible, but this helps a lot in the meantime.
Your function is frozen if there is no active invoke in progress. So no, ssh or minecraft server will not work, unless you make them communicate over Lambda invocations.
I also find it deeply ironic that their solution to cold starts is to keep the function running 24/7...
Could I include openssh and Apache in my Lambda instance? Maybe run a Minecraft server? :P