It depends on the nature of your desired interaction.
Do you need your user to focus on that particular item? If so, a full screen/modal-like interaction is still appropriate on desktop. e.g. http://interaction16.ixda.org/ (click on the hamburger menu). Another example is you're showing the user something complex, or something that needs a user response before they can continue (system dialog prompt).
The down side of fullscreen dialogs is that it slows down the user because they need to reorientate themselves with the new screen. For a web form where the user wants to input the info as fast as possible, regular form fields, with dropdowns, autocomplete fields would be much better. The user can still see the rest of the form content, as the relevant section expands to take up only as much room as it needs to.