That's an accurate description for certain values of the term 'computer'

Depends on your perspective really. In my experience, the word "Computer" strictly defines a tower and monitor to people I've encountered outside of the tech sector. While Laptops, Desktops, Phones, Game Consoles, etc are computers when people here Computer in a conversation they think of a tower and monitor or laptop. Most people wouldn't immediately connect their Phone or iPad as a computer in that sense.

To add: If were to be asked if I had a Computer in my house, and I didn't actually have my tower or MacBook, I would respond "No."

Google "computer", switch to images and tell me how many smartphones you see.