On the page you're on in the screenshot, open the browser Developer tools and use the inspect element tool to target the HTML element where the icon is. You may have to drill into it but you'll find the reference to it. Attached is an example.
Are there other thumbnails for other content type (map image layer, web map, etc) with a similar style?
I don't know if the entire thumbnail set is available for download as a separate bundle on an ESRI website but I would imagine that they are all installed someplace on your Portal's server installation so perhaps your GIS Admin could do some snooping around the server looking for them.
Apart from that, you could use the workflow I outlined to grab other thumbnails of interest.