The problem is now solved. There was a line missing in plugins/UserCountryMap/javascripts/visitor-map.js:

f = {
    nb_visits: 0.002,
    nb_uniq_visitors: 0.002, // this is the line
    nb_actions: 0.002,
    avg_time_on_site: 0.02,
    nb_actions_per_visit: 0.02,
    bounce_rate: 0.02
},

So you mean adding a nb_uniq_visitors: 0.002-line here:

I'm sorry, I edited really bad that comment... the line is the one specifying the value for unique visitors metric.

Exactly, @Findus23

Hi!

In its moment, unique visitors' points were not visible on the Visitor Map when it showed the cities.

After we corrected that error (the reason for this ticket to be created), we didn't check that everything was working perfectly. Now, one and a half years later, we noticed that the "big points" containing the largest numbers, were not visible on the map.

By making the following change to the file plugins\UserCountryMap\javascripts\visitor-map.js :

groups[g_id] = {
  nb_visits: 0,
  nb_uniq_visitors: 0, // this line
  nb_actions: 0,
  sum_visit_length: 0,
  bounce_count: 0
};

...the big points are finally being shown.