a quine is where the full source is reprinted in the display.
So in this case, the code to create this clock in your website is
<script>
(r=n=>setInterval(t=>{for(j=o="\n",y=5;y--;document.body['inne' +'rHTML']="<pre><"+(S="script>\n")+o+"\n\n</"+S)for(x=-001; x++<63;o+=`(r=${r})()`[j++].fontcolor(c?'#FF0':"#444"))c=x/2%4< 3&&[31599,19812,14479,31207,23524,29411,29679,30866,31727,31719 ,1040][(D=Date()[16+(x/8|0)])<10?D:10]&1<<(x/2|0)%4+3*y},100))()
</script>
which is also what is the clockface.