If you are wanting a similar interface as above you need to be exposing your inputs and outputs as Parameters, simply right click on them in model builder and select model parameter, then run the model outside modelbuilder. But you need to think about what you are asking:
Input data > Buffer > Project > Single part
The issue here is that you are passing a single dataset through the model. The interface above is proving a LIST of input datasets. If you read the help file, syntax section, buffer tool takes as input a SINGLE featurelayer. So what you are asking is impossible. Abdullah's idea of passing in a folder of shapefiles in more sensible, the user selects a workspace with datasets and then the iterator feeds out a dataset at a time into the rest of your model.