When wealthy, powerful Westerners like Bill Gates go meet rulers of small countries that are key for the West, it's a way of sending them as an emissary of the top Western financial elites. The top elites don't make such visits when they are older and senior, though they do when they are young and in their "apprenticeship", learning to run new world order. The current top elites typically have face-to-face meetings only with the leaders of the nations most important to them, i.e., UK, US, European, Russia, China, Japan.
Now note the difference in this pic - can you determine who is the Royal: imagine you don't know who the people are -
The people the Queen is meeting seem as comfortable in the situation as she is, at least. If you didn't know better, and I told you the man in the center with the blue tie was king of a greater Empire than the Queen's, I don't think one could argue differently based on the picture. Actually, his empire bankrolls her empire and the empires of all her nation's allies. Now the picture makes more sense. If you think of it in business terms, she's CEO, but he's the lead investment banker and chairman of the board of directors.
Now let's see the supposed reigning rulers of America meeting that Queen's grandchild and his wife:
The kids look far more authoritative, comfortable and self-assured than those "rulers" - who basically look like tourists, one yammering on about the food on the plane or something, the other trying to follow the royal small talk of the elites' future primary vassal.
Here's a real amazing one: this guy is much more uncomfortable than she is, and he's a billionaire mayor, and she's come to visit his town !
Even with his billions of net worth, Mike seems like he's having a hard time dealing with the meeting. He's definitely not "in charge".
Relax already - Phil looks like he just wants to go hang out on the terrace and knock back a Famous Grouse.