No Websockets Server for Arduino mkr1010?
Most websocket libraries work over a Client. Client is base class for all EthernetClient and WiFiClient classes. 

But why do you want to use a Websocket for communication of two MCU in the same LAN? Websockets are intended for communication over HTTP infrastructure (firewalls, proxies) to a web server in Internet or from browser to a web server. 

Use a basic TCP socket over Arduino Client.

WiFiClient object wraps a TCP socket. A normal TCP socket is connected to IP address and port. WiFiServer starts a listening socket on a port. If server on listening socket is contacted by a remote client socket, it creates a local socket connected with the remote client socket on a free port and returns a WiFiClient object wrapping the socket. Everything you write or print to a WiFiClient is send to that one remote socket.

If one of your client boards creates a WiFiClient and connects it to IP address and port of the WiFiServer on your 'server' board, then you get there a WiFiClient from server.available() and this two WiFiClient objects are connected. What you write/print on one side you read only from the WiFiClient object on the other side.

client socket

if (client.connect(serverIP, PORT)) {
  client.print("request\n");
  String response = client.readStringUntil('\n');
  Serial.println(response);
  client.stop();
}


server side

WiFiClient client = server.available();
if (client &amp;&amp; client.connected()) {
  String request = client.readStringUntil('\n');
  Serial.println(request);
  client.print("response\n");
  client.stop();
}