What you are seeing is actually a multi-select or multi-value drop down box in that example. It is not a single value drop down box like you are using in your code. Per the Select2 website, select2 will detect that you are trying to use a multi-select box and will automatically apply that styling instead of the default (drop down arrow, etc.).
If you in fact need a single value drop down box, there is no direct way to make it display with the formatting of the multi-select so that it looks like a regular input box. There may be a way to fake it by adding or removing CSS classes. I played around a bit but couldn’t find one.
Since you don’t want the formatting, the search box, or the multi-select capability (I’m assuming) you probably don’t need to use the select2 library.
Update: It looks like you’re not the first person to try to do this. They plan to add this feature but it might be a while:
https://github.com/ivaynberg/select2/issues/1345