How to make the Primary Menu stay the same in the PC and mobile versions of the Twenty Sixteen theme

Add below css in your theme style.css file, change font size if you need

@media screen and (max-width: 56.875em) {
    .main-navigation li {
        float: left;
        width: 33.333333%;
        text-align: center;
        font-size: 12px;
    }
}

UPDATE:

To make menu items inline apply floats on list elements not on nav tag
I checked using inspect elements and code i sent works fine. check that rule does not override by any other CSS in hierarchy.