The server comes in two flavors: the regular build that requires root permissions to run and the WeTek build that will run with system permissions.
You will need a recent version of Google Play Services (both apps at start will notify you if the provided GMS is outdated and take you to Play Store for update), with no Play Services these apps won't run because make use of some API present there.
This is how it works: once started the server uses UPNP to broadcast its presence, because of this client and server have to be connected to the same network and subnet. Moreover some routers don't route such packages between ethernet and client devices, it's a limitation of your network equipment not a flaw of the app.
Server

Setting it up is pretty straight forward, you just have to press on "START REMOTE CONTROL" button and, eventually, grant it root access.
You can access to settings from the icon in the top right, from there you can enable the automatic start of the remote control at boot and change the server name that you will see when you discover it from a client.
If for some reason the server cannot start you will be prompted with an error message, if everything goes fine you will see this

Client

To start discovery just tap on the big WiFi icon in the middle. You will get an error if you are not connected to a WiFi or Ethernet network. You won't see this discovery button if you device could not connect to Google Play Services.
In the contextual menu of the toolbar (in the top right) you can access to the settings where you can toggle haptic feedback and change the client name.
Once the discovery has finished and has found a server you will see this

Just tap on the device to connect to it.
Note: for security reasons in the server code I restricted access to a single client so you can't connect from two clients at the same time.
Once connected successfully you will be prompted with the remote controls

To close the connection to the server you can use the close button in the top right. The other button is used to send text to the server (it will do something only if the server is focued on a text input field)

Downloads
Remote Control Server 1.0 (Standard edition)
Remote Control Server 1.0 (WeTek edition)
Remote Control Client 1.0