Hello, the Raspberry Pi is required to establish the MQTT connection between your devices, because it runs Mosquitto MQTT broker.

Yes, you can also use a free CloudMQTT broker as I show in this thread: https://rntlab.com/question/using-cloudmqtt/

CloudMQTT is free for a couple of devices, after that it’s a paid service that’s I prefer to run my own MQTT Broker.

I meant can I use the sensors directly on the raspberry pi without the ESP8266-12E? I have the raspberry pi but I dont have the ESP8266-12E or Node MCU. Is it possible to proceed with the Raspberry pi receiving sensor values and publishing them to clients? 

Oh I’m sorry, I’ve misunderstood your question (often people want to eliminate the Raspberry Pi in that project). Yes, Node-RED has support for a lot of sensors, so you can read them directly with the Raspberry Pi.

• Which sensors do you want to use?
• Which clients are you going to publish to?

I will be using the same sensors in the project ie the MQ2 gas sensor and the motion sensor as per the project.
I’ll be publishing the data to the web clients.
Also is ESP 32 viable as ESP8266 replacement?

You can read those sensors directly with the Raspberry Pi. However, the Raspberry Pi doesn’t support analog reading, so you need to use an ADC to read analog values.
Yes, the ESP32 is the best choice for that application (I recommend it over the ESP8266).