Yeah...no. No they never met. And as cshock91 pointed out, the Inca existed long after the ancient Egyptians. And long after the Roman Egyptians. In fact, the Inca empire was just beginning to really expand and become an empire around the time that Columbus was born, they are very much contemporary and you can draw similarities between the Inca and Medieval Europe (they are very different, of course, but I mean similarities in the very broad sense, like the Inca had powerful and well-organized armies, built massive road networks, managed huge trade networks, etc.)

Now, actually looking at the site, I see they say a lot of Inca/pre-Inca. So ok, cool, they're not going for Inca specifically, but what do they mean by pre-Inca? The Andes were (and are) a massively diverse place and the Inca conquered a lot of independent states/societies/etc. with diverse languages, beliefs, and so on. Ancient Egypt was much more unified, in contrast, although there was diversity there too. The way that we describe periods in the Andes (Early Horizon, Early Intermediate Period, etc.) is derived from Egyptian scholars, but that's modern archaeologists using similar ideas to describe different societies, which is basically all that we do.

So, another pet peeve out of the way. Looking at the others, a lot of them come down to physics (pyramids, trapezoidal doorways, etc.) or ways to make your building secure in the event of earthquakes, and I hardly see how that means that something must be a shared tradition. These are common building types around the world. People are smart, and they come up with similar ways of solving the same problems. The pyramid is a simple and stable building form that was used all over the world for large strictures. And this website has picked out some of the most superficially similar ones to show you, when the more typical ones in the Andes looked more like this. The use of pyramids was also quite different; in Egypt, they were burial mounds. The Andes, they were first and foremost temples where religious ceremonies, public meetings, etc. took place and they were often modified over the centuries as their needs grew. There were definitely elite burials in them but that's because they were important places for ancestor worship, not places built specifically for that burial.

On that note, mummies. Mummification was massively important to the Egyptians, and the specific processes (e.g. removing organs) were a major part of the process. Andean mummies were wrapped in textiles along with grave goods (also a very common practice around the world) and buried in dry environments so that the bodies mummified naturally (or the Inka sacrificed some children on glaciers, which also mummified them through ice). The earliest known evidence of treatment of the dead in a way meant to preserve them in the Andes are the Chinchorro mummies, which pre-date Egyptian mummies by millennia.

And this is another important point: we see indigenous development of these things in both Egypt and the Andes. If Atlanteans or aliens or whoever suddenly showed up, then we would see very similar things appear at the same time in both places. But we don't. The author of this website has picked out some things that vary tremendously through time and presented them as being equivalent, but they each developed gradually in their own places and you can see this progression through time. I'm no scholar of art and iconography so I can't address that stuff as well, but knowing the Andean stuff fairly well, all these similarities seem pretty superficial to me and have examples from elsewhere in the world, and more interestingly point to shared ideas about life and the universe--at a very basal level--that stretch very, very deep into the human past.

One last point I want to make has to do with all these "archaeologists are hiding the truth because X, Y, Z" arguments. I see them all the time and they make no sense to me. If I could solidly establish some sort of connection between these two vastly different places, it would make my career. I would be famous, and probably rich too. Why would I try to suppress that? To fit some dogmatic old establishment ideas? We're constantly throwing out the establishment ideas and replacing them with new ideas (e.g. in my dissertation I argued that two of the biggest 20th century names in the field were just plain wrong in one study), but to the general public the new ideas don't seem very different from the old. We must follow from the evidence and go where the evidence points us, and if the evidence simply isn't there for some radical idea, we don't entertain it for long. If, in the future, we find evidence for it, then the old ideas will be thrown out and we'll come up with new ones. We do it all the time, and would certainly do it for something as big as 5000 year old continental connections, if there were any solid evidence for it.

Sources:

My stuff just comes from a few general sources on the Andes, mostly.

Moseley, Michael E. 2001 The Incas and their ancestors: The archaeology of Peru, 2nd edition. New York: Thames and Hudson.

Quilter, Jeffrey. 2014 The Ancient Central Andes. Routledge, London.

This is another absolutely excellent book you should check out to see similarities around the world. Trigger was an expert on ancient Egypt (and other places) and had a truly masterful understanding of comparative archaeology around the world. This is one of his two magnum opuses (opii?) and gives a really good introduction to the archaeology of states/"civilizations" around the world. Take a look at it to see the cross-cultural similarities that are acknowledged by all archaeologists:

Trigger, Bruce G. 2003 Understanding Early Civilizations. Cambridge University Press, Cambridge.

Most of what that article is pointing to are artifacts of the Incan Empire, not the pre-Inca cultures. The empire was founded in 1438 by Pachacuti, about 3 millennia after the pyramid of Khufu. There is no way that these cultures met, not just because of the vast oceans and great distances, but they were also separated by thousands of years. Things like precision stone work, solar religions, animal symbolism, golden burial masks, and obelisks with writing on them can be found in civilizations all over the world.
The reason that the Egypt/Inca similarities are "being ignored by American and Western scholars" is that these similarities don't mean anything. You can find just as many differences between the cultures as similarities.