If you disable JavaScript, DateInputWidget should fall back to being a regular date input field and let the user type in the date. Currently, however, the field becomes completely unusable due to the CSS:
.mw-widget-dateInputWidget.oo-ui-textInputWidget input { -webkit-user-select: none; -moz-user-select: none; -ms-user-select: none; user-select: none; }
See src/mediawiki.widgets/mw.widgets.DateInputWidget.less line 14.
This CSS should be applied by the OOjs-UI JavaScript, not in the LESS file (or overridden by a .client-nojs rule).