Just a quick fix: WL 11 doesn't like the two-stage form. You can make the app work again by changing the layout to a single form page. To do that, simply replace all code before the Module starts with the following:

CloudDeploy[FormFunction[{
   {{"file", "Upload a VASP POSCAR or CONTCAR file here:"} -> <|
      "Interpreter" -> "UploadedFile"|>}, {
    {"sysdim", "Periodic repetitions"} -> <|
      "Interpreter" -> 
       Restricted[
        DelimitedSequence["Integer", 
         " " | "," | ";" | "/" | "x" | "X"], 3], "Input" -> "1x1x1"|>,
    {"retractq", "Retract atoms to cell?"} -> <|
      "Interpreter" -> "Boolean", "Input" -> False|>,
    {"addq", "Add periodic duplicates of atoms?"} -> <|
      "Interpreter" -> "Boolean", "Input" -> False|>,
    {"atomrad", "Atom radius"} -> <|"Interpreter" -> "ComputedReal", 
      "Input" -> 0.4|>,
    {"bonddist", "Maximum bond length"} -> <|
      "Interpreter" -> "ComputedReal", "Input" -> 2.1|>,
    {"monobond", "Want to pick your own bond color?"} -> <|
      "Interpreter" -> "Boolean", "Input" -> False|>,
    {"bondcol", "Bond color"} -> <|"Interpreter" -> "ComputedColor", 
      "Input" -> GrayLevel[.8]|>,
    {"bondrad", "Bond radius"} -> <|"Interpreter" -> "ComputedReal", 
      "Input" -> 0.1|>,
    {"linecol", "Cell outline color"} -> <|
      "Interpreter" -> "ComputedColor", "Input" -> Black|>,
    {"linerad", "Cell outline radius"} -> <|
      "Interpreter" -> "ComputedReal", "Input" -> 0.02|>
    }},

My initial motivation for the two-step process was to allow users to select a file once, plot the structure, then go back and change the layout without having to find their file again. (Since that can be a hassle on a phone in particular.) If anyone wants to play around with a solution that allows for that in WL 11, feel free to post here!

@Bianca Eifert Really amazing post indeed! Is it possible to have 3D interactivity (like rotate or zoom) after the final output?

@Vitaliy Kaurov Changing PNG to HTML is really useful. Are there more options available to format the final output? For instance, if we want to compose two or more than two outputs from the same Cloud app?

Thank you, and thanks especially for the movie!

In case anyone's wondering: Selecting a bond colour as shown in Vitaliy's movie doesn't do anything because unfortunately you also have to check "Want to pick your own bond color?". I know that's not pretty, but I couldn't figure out how to make an input field that would accept input that's either a colour or Automatic (or something along these lines). The "default bond colour", if you will, is not really a colour, but rather the instruction to use the atom colours and make two-coloured bonds. There's probably a more intuitive way to do this. The good news is that once you've generated the plot, you can go back and edit the layout options without having to pick out the file again. (And if you really need to fine-tune the layout, you're better off with Crystallica anyway.)

Vitaliy, is there an output variety I could use instead of "PNG" or "HTML" that actually produces an object that can be rotated and resized like a Graphics3D object in a notebook?

I see, thank you. I remember now that I've seen examples of an entire Manipulate inside a CloudDeploy. But I can't get that sort of thing as a result to a FormFunction, is that correct?

Oh, that actually works! I don't recall what I was trying earlier that didn't work, but this is good to know. Thanks!

Excellent post, @Bianca Eifert, thanks for sharing! I added a small movie to show what people should expect. I made a slight modification to the code with "PNG" changed to "HTML"

CloudDeploy[FormFunction[X, Graphics3D[Y] &, "HTML"]]

which centers the output graphics.