Media Engagements in the UI is actually equivalent to Media Views in the API, so you should be able to use Media Views the metrics from the API do do this calculation.
Specifically, looking at our Derived Metrics page, Media Views is defined as such:
{Media Views} = promoted_tweet_timeline_media_views + promoted_tweet_search_media_views + promoted_tweet_profile_media_views
This metric has undergone several naming changes in the UI, for compatibility reasons we have kept the original name through the API.
Note that for VIDEO_VIEWS, we do not currently have the ability to calculate media engagements alone, and our team is working on it.