Inserting a javascript game into a page?

Yes, you can certainly put this game in a drupal page. The code below is from a website I developed a few years back; it creates a memory game similar to what you have linked above. The images are numbered 1.jpg, 2.jpg, etc. This script asks the visitor to press a button below the game to start. Set input filter to full html.

<SCRIPT LANGUAGE="JavaScript">
<!-- Begin
var pics = new Array();
for (i = 0; i <= 18; i++) {
pics[i] = new Image();
pics[i].src = 'http://site.com/images/image' + i + '.jpg';
}
var map=new Array(1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18);
var user = new Array();
var temparray = new Array();
var clickarray = new Array(0, 0);
var ticker, sec, min, ctr, id, oktoclick, finished;
function init() {
clearTimeout(id);
for (i = 0; i <= 35 ;i++) {
user[i] = 0;
}
ticker = 0;
min = 0;
sec = 0;
ctr = 0;
oktoclick = true;
finished = 0;
document.f.b.value = "";
scramble();
runclk();
for (i = 0; i <= 35; i++) {
document.f[('img'+i)].src = "http://site.com/images/image0.jpg";
   }
}
function runclk() {
min = Math.floor(ticker/60);
sec = (ticker-(min*60))+'';
if(sec.length == 1) {sec = "0"+sec};
ticker++;
document.f.b.value = min+":"+sec;id = setTimeout('runclk()', 1000);
}
function scramble() {
for (z = 0; z < 5; z++) {
for (x = 0; x <= 35; x++) {
temparray[0] = Math.floor(Math.random()*36);
temparray[1] = map[temparray[0]];
temparray[2] = map[x];
map[x] = temparray[1];
map[temparray[0]] = temparray[2];
	  }
   }
}
function showimage(but) {
if (oktoclick) {
oktoclick = false; 
document.f[('img'+but)].src = 'http://site.com/images/image'+map[but]+'.jpg';
if (ctr == 0) {
ctr++;
clickarray[0] = but;
oktoclick = true;
} else {
clickarray[1] = but;
ctr = 0;
setTimeout('returntoold()', 600);
	  }
   }
}
function returntoold() {
if ((clickarray[0] == clickarray[1]) && (!user[clickarray[0]])) {
document.f[('img'+clickarray[0])].src = "http://site.com/images/image0.jpg";
oktoclick = true;
} else {if (map[clickarray[0]] != map[clickarray[1]]) {
if (user[clickarray[0]] == 0) {
document.f[('img'+clickarray[0])].src = "http://site.com/images/image0.jpg";
}
if (user[clickarray[1]] == 0) {
document.f[('img'+clickarray[1])].src = "http://site.com/images/image0.jpg";
   }
}
if (map[clickarray[0]] == map[clickarray[1]]) {
if (user[clickarray[0]] == 0&&user[clickarray[1]] == 0) { finished++; }
user[clickarray[0]] = 1;
user[clickarray[1]] = 1;
}
if (finished >= 18) {
alert('You did it in '+document.f.b.value+' !');
init();
} else {
oktoclick = true;
	  }
   }
}
//  End -->
</script><style>

table {
  margin: 0;
  width:85%;

}
tr{padding: 0;}
td {padding: 0;}
</style>

<hr>

<CENTER>
<Table border=1 bgcolor="#dddddd"><tr><td>
<table border=0 cellpadding="0" cellspacing="0">

<form name="f"> 
<script language="javascript">
<!-- Begin
for (r = 0; r <= 5; r++) {
document.write('<tr>');
for (c = 0; c <= 5; c++) {
document.write('<td align="center">');document.write('<a href="javascript:showimage('+((6*r)+c)+')" onClick="document.f.b.focus()">');
document.write('<img src="http://site.com/images/image0.jpg" name="img'+((6*r)+c)+'" border="0">');
document.write('</a></td>');
}
document.write('</tr>');
}
// End -->
</script>

</table> </tr></td></table>
<br>
<font color="#0000cc"><b>Press here to start ---></b></font> <input type="button" value="	Go	 " name="b" onClick="init()">
</form></center>