https://github.com/ezura/sample6/blob/master/websocket-server/main.rb

main.rb

require "em-websocket"
require 'json'
require 'sinatra/base'
require 'thin'

$stdout.sync = true

# FIX_ME: port とか host とか直打ちしない
EventMachine.run { 
  @globalChannel = EM::Channel.new
  @channels = Hash.new { |hash, key| hash[key] = EM::Channel.new }

  class App < Sinatra::Base
    get '/' do
      "Hello!"
    end

    # locahost:3001/states/1
    post '/states/:id' do
      # params[:id]
      params = JSON.parse request.body.read
      puts params
      @globalChannel.push "@globalChannel.push"
    end
  end

  EM::WebSocket.start(host: "localhost", port: 3002) do |ws|
    ws.onopen {
      sid = @globalChannel.subscribe { |message| ws.send(message) }

      ws.onmessage { |msg|
        recieve_data = JSON.parse(msg)
        channel.push msg
      }

      ws.onclose {
        @globalChannel.unsubscribe(sid)
        # @channels.values.each { |value| value.unsubscribe(sid) }
      }

      @pushData = lambda { |data| @globalChannel.push data }
    }
  end

  puts "------------ #{Process.pid} ------------"
  App.run!(:port => 3001)
}

# error 内容
# NoMethodError - undefined method `push' for nil:NilClass:
#	 websocket-server/main.rb:23:in `block in <class:App>'

解決しました。
@globalChannel のスコープの問題でした。