KAVYOMEE No, you have to buy a ticket from Chiasso (the border station with Italy) to Milano Centrale.
The easier way to buy this ticket is the SBB Mobile app on your smartphone, this is an “Arcobaleno Transfrontaliera” ticket and it cost 6 CHF (2nd class) for an adult. This ticket is only valid on regional trains (the RE80 is a regional train).
Please note that this ticket is only valid 4 hours, you must select the right train from the border station of Chiasso, the 17:02 train leaves Chiasso at 17:31. The ticket will be valid until 21:31 and you could also take the next train if you miss the connection in Lugano.