Почти там - вам нужно jQuerify цели:
var cnt = 0;
$("#map").on("click", function(e) {
e.preventDefault();
cnt++;
if (cnt > 3) {
alert("You had your 3 gos");
}
else {
var $tgt = $(e.target);
// console.log($tgt.attr("alt"));
$("#turn"+cnt).val($tgt.attr("title"))
}
});
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<img id="goal" src="http://pngimg.com/uploads/football_goal/football_goal_PNG24.png" usemap="#goal-map">
<map name="goal-map" id="map">
<area id="test" href="#" alt="300 points" title="300" coords="483,50,584,146" shape="rect" />
<area class="a" href="" alt="300 points" title="300" coords="110,49,11,145" shape="rect" />
<area class="a" href="" alt="200 points" title="200" coords="13,148,110,238" shape="rect" />
<area class="a" href="" alt="200 points" title="200" coords="484,149,584,237" shape="rect" />
</map>
<br/>
This is the input field that needs to be filled:
<p>Turn 1:
<input type="text" id="turn1"></p>
<p>Turn 2:
<input type="text" id="turn2"></p>
<p>Turn 3:
<input type="text" id="turn3"></p>