Travel time

Customs takes no time at all. Customs is the check on the contents of your luggage. It is a random check only, 99% of people are not stopped.
Immigration (aka passport control) is the check on whether you are allowed into the country. This typically has a long wait and can take 30-90 minutes. Except, if you are flying from a Schengen Area country, there is no immigration check. Where are you flying from?
Plus, if you are flying intercontinental, flight arrival could be +/- 1 hour depending on winds.

12:10 land Milano airport (Malpensa I assume)
Disembark, immigration, emerge from the airport: 13:00 (on a good day, 14:00 on a bad day)
Local train into Milan, arrive Milano Centrale: 14:00-15:00
Train to Genoa takes 1½ hours, but you need to wait for the next train: 16:00-17:00 (if everything works)
Taxi to cruise terminal, must be at least 30 minutes: 16:30 to 17:30
Sorry, your ship is just untying, too late ☺

On the way back:
08:00 dock, 08:30, disembark (if you are lucky), 09:00 at Genoa station, 11:00 Milano Centrale, 12:00 Malpensa.
How long in advance do you need to check-in for this flight? Could be 1-3 hours.
Sorry again ☺☺

I think you need some overnights in Genoa or Milan.

You say the ship leaves at 5 pm. When do you have to be there to board?

I don't think you have near enough time on either end of your cruise. I'd book flights to arrive a day early and leave a day later. You could arrive Milan, stay the night, take the train to Genoa in the morning, have lunch and not be pressed to make the cruise.

I do not cruise, but I would never, ever count on being at the Milan airport two hours after my ship was scheduled to dock in Genoa. There could be a bit of a delay at the dock. You might not be the first one off the ship. You have to get from the dock to the appropriate rail station. You have to wait for the next train, and it appears that they are sometimes more than an hour apart.

Also, perhaps I'm missing something, but what I see on the train schedule is that it's more like 3 hours from Genoa to Milan-Malpensa.

it's more like 3 hours from Genoa to Milan-Malpensa.

The OP quoted 1½ hours Genoa to Milan. That's to "Milano Centrale" in the city centre. Then add the time to get to Malpensa airport, with waits between trains, and you get 3 hours

I am taking a cruise out of Genoa Italy, but it is cheaper to fly into
Milan. My plane arrives at 12:10 pm and the ship leaves at 5 pm....by
train Milan is an hour and half away from Genoa.

If you are flying into Milan Malpensa, you are more like 3 hours and not 90 minutes from Genova.

This is the end I'd be concerned about. Even if you can make the ship - and I don't see as you can - it's not all that uncommon for flights to be significantly delayed or even cancelled. It would be a LOT safer to arrive in Italy the day before your cruise.

I'd be just as concerned about having just 5 hours between docking and your flight out of Milan as well. I think you've quite seriously underestimated just how long it's going to take from Malpensa to port and vice versa.

(Edited)

When planning flights, my rule of thumb is that I want to be in the departure city on the night before the flight leaves. Similarly, if I absolutely had to be somewhere other than my flight arrival city, I would plan to be there on the next day.

Please rethink this. Arrive the day before the cruise. If you miss the embarkation it will be costly arranging to get to the first port of call to catch up with the ship. Not to mention what a lousy way to start a cruise.

If you miss the flight home from Milan, are you prepared to pay the cost of flights home bought that day? There goes your “cheaper” way of doing this.

Way to close for comfort either end. I seem to rarely have flights depart or arrive on time and would never do such a long flight on the day of a cruise. Yours, in particular is way to short of time even if things don't go wrong.
Also, depending on the itinerary, and the unfortunate current status of human cargo ships at sea, I wouldn't plan to fly out the same day as arrival - unless you have good travel insurance. You have more cases in the Med of delayed arrival back in port due to rescues at sea than we seem to have in North America. Yes, it is added expense and vacation time, but look at it as an extension of your travel.
If you want alternative opinions, join CruiseCritic (sister company to TripAdvisor) but full of cruisers and experts and ask there.

Contact your cruise line or the travel agent who booked your cruise. Often the cruise company will offer transportation from a major airport to the ship--for a hefty price. See if your cruise line offers this service from Malpensa. If there isn't anything offered, then I agree with the other comments--you do not have enough time to get to your ship from Malpensa if it leaves at 5 p.m.

Conventional wisdom is to arrive a day before your cruise departs. What if there is bad weather or mechanical that delays you? This is true both coming and going, but especially for arrival because if you miis the ship, it’s a nightmare. Check the stories over at www.elliott.org about people who cut it too close. They do not get financial compensation.

Hopefully your flight is not yet booked.