There are other docs saying otherwise as well. The only way to be sure is to eliminate that router. Gigabit switches are very cheap and you will find a use for it.
The other possibility is the high bitrate of an MKV on a congested network (best scenario is 10.7 MB/s hence why I recommend Banana Pis). If you want the maximum speed from an ext4 drive over a network from a Pi you should use ftp (mini guide) as the share method for Kodi, according to these benchmarks. Kodi has built-in options for connecting to FTP.
The other possibility is the high bitrate of an MKV on a congested network (best scenario is 10.7 MB/s hence why I recommend Banana Pis). If you want the maximum speed from an ext4 drive over a network from a Pi you should use ftp (mini guide) as the share method for Kodi, according to these benchmarks. Kodi has built-in options for connecting to FTP.