Such a file explorer component would require server-side logic to create the list of files. Since this is highly specific to the server, framework, application, authentication, user roles and permissions (and probably a lot of other factors), this is something that the application needs to generate. Once you have enumerated the files and folders, you can easily show them in a control like a TreeView or TreeList.
In the meantime, you can monitor the feature request for such a widget in the following page by using the Follow button (I have already added your vote): https://feedback.telerik.com/kendo-jquery-ui/1358399-fileexplorer.
You can also try instantiating the file browser widget used in the editor as someone did in this thread or like in this example, but it is not something we support outside of the editor.
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