Bluray was bad example , but let's just say a HDMI source, and it doesn't need or even want it stream outside of lan
The answer is the same for any HDMI source.
You dont decode and render source material to a live HDMI stream and send it over a LAN, the bandwidth is huge and most LAN,s cannot handle it.
The most common LAN in the home is Gigabit, even 1080p on a Live HDMI feed is at least 3 times that .... for 4K it is up to 18 times that.
It is very common these days for people to stream content over their LAN, but you stream the original data in its compressed container, i.e. ISO, MP4, MKV, or whatever container your content comes in, to a device that then unpacks , decodes, and renders the live stream over a HDMI interface to a screen.
(In the case of your tablet, you get your content into a format suitable for streaming, then get an app like VLC and play it from your network, the app does the decoding and rendering on your tablet.)
You dont send the actual Live Stream over the LAN, that would be a horribly inefficient way to do things.
Note: this is impossible in any case, you have a Gigabit network , one single live HDMI stream is a minimum of 3 Gigabits....you stream original packaged content, NOT a Live HDMI feed.
Note 2: Nobody sells content in an MKV package, but this is a very popular container for home ripping your own content for storage on a NAS or computer. Google a program called " makemkv"