Most of what we see around us is made up of molecules, in various forms. Molecules form when atoms share electrons. There are different types of atomic bonds, some in which one atom forms a discrete bond to another atom, (covalent bond) or, ones in which they form a general shared pool of electrons (metallic bond). The physics and chemistry of how and why atoms form bonds is a fascinating subject, but the short story is: everything we see around is in the form of a molecule, atoms connected together. Normally, the only thing we encounter that is not in the form of molecules are the inert gasses, such as helium and argon, but unless you are a blimp pilot or a welder, those things don't come up often.
But lets expand our vision a little. What would our universe look like, on the whole, if all atoms were inert, if atoms could not form bonds, and if only physical forces like heat and pressure determined how atoms behaved. How would this change the major physical processes of our universe?
The answer is, it wouldn't. Molecular structures are so rare, and so unimportant in our universe, that a theoretical "outside observer" looking at our universe would probably not even know they existed. A large scale model of our universe, covering the existence of galaxies, stars, interstellar gas, black holes, neutron stars, gamma ray bursts, and even brown dwarfs and most planets. Most of the noteworthy events in our universe occur without molecular processes being important at all.
Putting aside the issue of dark matter for a moment (but we will return to it in a bit), lets look at a representative sample of what is in space: our own Solar system. The sun makes up more than 99.8% of our solar system, and most of the remaining 0.2% is Jupiter and Saturn. Stars exist in the form of plasma, atoms where the electrons have been stripped from the nuclei, due to heat, and where the positively charged nuclei and negatively charged electrons never cool down enough to form atoms, let alone form molecular bonds. The gas giants, such as Jupiter and Saturn, are cool enough to form molecules, but they are shaped by gravity. The fact that some of their atoms are in the form of molecules like molecular hydrogen or methane does increase their density, but on the whole, they can be looked at in terms of physics, not chemistry. Even the smaller planets, such as our own earth, are mostly held together by gravity. We have to go down the scale, to comets and asteroids, to find bodies that are held together mostly by molecular forces, and not by gravity. These small, not gravitational bodies make up maybe less than one-millionth of the mass of the solar system.
On a larger scale, our galaxy is made up of stars, clouds of gas, and stellar remnants. Black holes and neutron stars aren't even made up of "normal" matter, let alone anything that can form atoms. Stars have already been discussed. Gas clouds are in the form of both atomic and molecular elements, but if those molecules were turned into atoms, they would behave approximately the same: although they may be more diffuse, and thus less likely to collapse under their own gravity into a star. So without molecular bonds, stars might be less common, or form under different circumstances. But on the whole, our universe would still look like it does.
To return to the subject of dark matter: most scientists believe, based on the gravitational anomaly in how galaxies rotate, that our universe is made up primarily of dark matter, matter that interacts with us only through gravity, but is not detectable in other ways. And if we can imagine a dark matter universe, where dark matter scientists become aware of other forms of matter and somehow begin to investigate our universe using incredibly advanced equipment, they might start getting a peek at what is going on here. I can imagine them discussing how these exotic, almost theoretical objects called "stars" have a gravitational impact, and radiate away energy that to them is as inconsequential as neutrinos are to us. And these super-advanced scientists with their super-advanced equipment might even be able to detect that some of this matter forms shadows orbiting these stars. But all of the molecular world: the fact that atoms can form chains and loops with each other, can concentrate into interacting patterns, would be invisible to them. At most, they might look at one of thse objects and realize it is a slightly different shape and size than it should be, and chuckle at the rounding error that makes their calculations in error.
The world we are familiar with, the world we live in, is from a large scale viewpoint, almost an afterthought or minor side effect of the physical processes that the universe is mostly run on.