You may get it from YouTube Analytics API so far, based on the videoId, I created below a function in Google Apps Script for this data.
function videoShareCount(channelId,videoId) {
var today = new Date();
var startDate = YouTube.Videos.list('snippet',{id:videoId}).items[0].snippet.publishedAt;
var todayFormatted = Utilities.formatDate(today, 'UTC', 'yyyy-MM-dd')
var startDateFormatted = Utilities.formatDate(new Date(startDate), 'UTC', 'yyyy-MM-dd');
var analyticsResponse = YouTubeAnalytics.Reports.query(
'channel==' + channelId,
startDateFormatted,
todayFormatted,
'shares',
{
dimensions: 'video',
filters: 'video=='+videoId,
});
if (analyticsResponse.rows)
return analyticsResponse.rows[0][1];
else
return 0;
}