what the plugin is this

Do you mean the linked logos for each of the sites within the multisite network at the very top of the page?

If so, I don’t think it is from a plugin. It looks like it was custom developed for these sites. The html to build it is a simple ordered list with the id “network-bar”. All of the CSS to style it is contained within the theme’s stylesheet. It would not be difficult for an experience developer to build something similar, and you can get the same functionality using WordPress’s custom menu feature with some custom css.

+1 to cubecoour
It does look to me as manually inserted code into the theme.

It’s quite simple though.. and doesn’t involve any special developer ??
All what you need is to insert into the header.php or page.php(or index.php) into particular place, depending on your theme, this code snippet (but you are not limited to it, feel free to alter it)

<div id="My-Top-Network-Bar">
		<ol>
			<li id="bar-mediaite"><a href="https://www.mediaite.com/">Mediaite</a></li>
			<li id="bar-gossipcop"><a href="https://www.gossipcop.com/">Gossip Cop</a></li>
			<li id="bar-geekosystem"><a href="https://www.geekosystem.com/">Geekosystem</a></li>
			<li id="bar-styleite"><a href="https://www.styleite.com/">Styleite</a></li>
			<li id="bar-sportsgrid"><a href="https://www.sportsgrid.com/">SportsGrid</a></li>
			<li id="bar-marysue"><a href="https://www.themarysue.com/">The Mary Sue</a></li>
			<li id="bar-thejanedough"><a href="https://www.thejanedough.com/">The Jane Dough</a></li>
			<li id="bar-thebraiser"><a class="bar-current" href="https://www.thebraiser.com/">The Braiser</a></li>
		</ol>
	</div>

And style it in anyway (if you know how) by css referencing to #My-Top-Network-Bar ID.

Hope that helps..