Triggering Blue Iris (Camera Software) with a nodeMCU (esp8266)

  if (client.connect(BIserver, 818)) {             // (81) Port number of the Blue Iris web server //CHANGE THIS if you don't use port 81.

If you are going to have useless comments, they MUST be accurate useless comments.

    client.print( "&trigger&user=");

The data in the GET request is usually in the form of name=value pairs, separated by &s. What is the value associated with trigger?

which I don't think works with the nodemcu

If the code compiles, WiFiClient is a class defined in the ESP8266WiFi header file, so it must be able to work with the ESP8266 device.

Are you able to connect to the camera server?