The API has changed indeed.
It should be like this.
https://graph.facebook.com/?id=https://stackoverflow.com&fields=engagement&access_token=user-access-token
You need an access token. If you have a Facebook, go to https://developers.facebook.com/ and make an app.
Graph API Explorer
Then click "Graph API Explorer".
Get Token
and "Get Token" (Get App Token). That's it.
If you use JavaScript for a count, it's will be something like this.
// split('#')[0] : Remove hash params from URL
const url = encodeURIComponent( window.location.href.split('#')[0] );
$.ajax( {
    url : '//graph.facebook.com/?id=' + url + '&fields=engagement&access_token=user-access-token',
    dataType : 'jsonp',
    timeout: 5000,
    success : function( obj ) {
        let count = 0;
        if ( typeof obj.engagement.reaction_count !== 'undefined' ) {
            count = obj.engagement.reaction_count;
        }
        // do something with 'count'
    },
    error : function() {
        // do something
    }
} );
There are other count types such as comment_count and share_count.
See https://developers.facebook.com/docs/graph-api/reference/v3.2/url
Is there any way to receive a count without sending an access token?
I wanna know that myself lol
UPDATE:
Thanks to Anton Lukin.
Yeah. I shouldn't show an access token. It must be hidden. I feel very foolish.
So now quick's answer. This really works without the token!
My final (I hope will be final) answer is like this.
// split('#')[0] : Remove hash params from URL
const url = encodeURIComponent( window.location.href.split('#')[0] );
$.ajax( {
    url: '//graph.facebook.com/?id=' + url + '&fields=og_object{engagement}',
    dataType : 'jsonp',
    timeout: 5000,
    success : function( obj ) {
        let count = 0;
        try {
            count = obj.og_object.engagement.count
        } catch (e) {
            console.log(e)
        }
        // do something with 'count'
    },
    error : function() {
        // do something
    }
} );
One point here is that when nobody has ever shared the targeted page, 'og_object.engagement' isn't even defined.
I thought I'd get 0 as a return valule. But that's not the case.
So let's use try-catch.
Now my only concern is API Limits. If your site gets a lot of pageviews, this updated version may not work..