Can I access the file stream shared folder using Listeners in case of AlwaysOn cluster environment?
I do not believe your extracted quote is relevant to your problem.

Your issue could be that your listener has multiple IP addresses. Under the default configuration, the listener will have multiple A records in DNS and your client will cache only one of them. Each time the cache expires it will randomly grab one of the IP addresses and sometimes it will get the active IP and other times it will get the one that is offline.

This is the purpose behind the MultiSubnetFailover parameter that the listener acknowledges.