It almost drove me nuts that I couldn’t make the events countdown to look as in the demo.

Turns out the necessary CSS is in the paid plugin “Events Calendar PRO“, and not in the free version.
After copying the following CSS from your demo site to my own child-theme style sheet, it finally looked right.

.tribe-countdown-timer h3.tribe-countdown-complete,
.tribe-countdown-timer span.format,
.tribe-countdown-timer span.tribe-countdown-seconds {
    display: none
}
div.tribe-countdown-timer {
    line-height: 1.5em;
    min-height: 60px;
    padding-top: 10px;
    text-align: center
}
div.tribe-countdown-number {
    color: #000;
    float: left;
    font-size: 2.4em
}
span.tribe-countdown-under {
    color: #666;
    font-size: 10px;
    font-weight: 500;
    text-transform: uppercase
}
div.tribe-countdown-colon {
    color: #666;
    float: left;
    font-size: 1.5em;
    padding: 0 4px
}
div.tribe-countdown-right {
    float: left
}
div.tribe-countdown-text {
    clear: both;
    margin: 0 0 10px
}