I can't open up these projects in unity.

The page has a button that says Open in Unity. Which when I do that it opens unity but goes to a blank load/new page not actually opening the project.

Try to open it directly from you HD… in my computer it’s in C:\Users\MyUsername\AppData\Roaming\Unity\Asset Store-5.x\Unity Technologies\Unity EssentialsSample Projects\Unity 5 Survival Shooter.unitypackage
Maybe you have it on a similar location

Another thing you could try is to use the browser that is inside unity and try to open from there.