What word or phrase describes this musical instrument?

That would be called a barrel organ. The person who plays it is called an organ grinder. I've only seen them on TV and in movies, and I've never seen the fortune card part of it. Just the musical instrument.

(Barrel organ - Britannica.com)

The answer to the OP's question is definitely "Barrel Organ" but there is a degree of confusion about what this term means and also around the terms Barrel Organ and Hurdy-Gurdy. In particular there is a comment discussion going on between @DarrelHoffman and @Édouard. I was going to add my own comment when I found this site belonging to a maker of barrel organs from which I copied the following paragraph:

To clear up some common misconceptions, these pages are devoted to 'organs' - that is, instruments with pipes that sound when air is blown through them, just like a church organ, but a lot smaller! 'Barrel Organs' were a common sight years ago, and some did contain air-blown pipes, but the majority of these were actually very large versions of a musical box - as revealed by the 'metallic' sounds that they produced. Another name sometimes wrongly applied to Busker organs is 'Hurdy Gurdy'. This is actually a mechanical violin, where a rotating wheel takes the place of a bow, and notes can be sounded by operating keys to press the violin strings onto the wheel.

This said so much that I wanted to say and with so much authority that I thought I should share it with the community. The only thing I would add is that true hurdy-gurdies are instruments which need proper musical skills to play whereas barrel organs of all types are hand-cranked mechanical instruments where the tune is determined by spikes on a rotating drum or holes in cards or paper. For those who are interested I would suggest that they enter "hurdy-gurdy" into a search engine. There is a wealth of information and demonstrations out there.