Outdoors at the Beach Rotana in Abu Dhabi, they had two of those screens big enough that they might have been visible from other planets, so that you might picture some far-flung alien with a mighty telescope muttering, "I just love that Iniesta".
As maybe 200 melting sorts in night heat settled into picnic tables for Spain and Italy on Sunday night, you might have sensed versions of the scene replicated almost all over the world. From Barcelona to Beijing to Bogota, you would find big screens and small gatherings and large anticipation centred upon Spain.
To the world now, Spain represents the established and the assumed and the understood even as it has used such a velvet hammer toward dominance that it never has become grating.
On screens big and small, the world would see Iker Casillas lift the trophy and the team start hopping, the third time they have done so in a world full of players dreaming of doing it once.
All over the planet, fans could see the exultant Spanish supporters respond to goals in the kind of mass bouncing that makes sport so irresistible, and could ponder that some of those fans might have travelled to five countries since 2008 without ever seeing their national team concede in a knockout match.
The world could see Spain's bench spill out onto the pitch for yet another hug-a-thon, and might think of the drive required to produce three straight major international cups when the human tendency is to get comfy with success.
We watched this greatest-team-ever business, and in a world of profligate TV channels and fragmented world views, this might be among the last such connectedness we get.
Even from afar … even as the last suspense drained out of the match when Italy went to 10 men and Spain went to three goals … even as the Abu Dhabi crowd probably resembled others in going mostly tepid … even as it couldn't match its boisterousness of Thursday night while Italy upset Germany …
You could feel plugged into something well-defined.
Most everybody knows what Spain football means, circa 2012.
Nobody much remembers - or talks about - the Wednesday of June 28, 2006.
As of that day, Spain had just lost 3-1 on a Tuesday night to Zinedine Zidane's France in the World Cup round of 16 and had remained a major football nation that somehow, some way, had not visited even a World Cup semi-final since 1950 (and not a real one, ever).
Nobody remembers that the headlines included, "Broken Dreams", "Failure" and "Back Home, As Always". (They don't write headlines like that anymore in Spain.)
The foreseeable scene of youths jumping in a fountain after a defeat, police drawing batons and youths throwing bottles? If that happens now, it's in mad glee.
It's only a marker anymore to look back at El Pais of that Wednesday, which lamented "the Spain of always, the same which always falls in the top tournaments, a victim of its own misfortune and incapable of beating teams of higher standard".
The sports daily Mundo Deportivo bewailed "not even the quarter-finals", when by now quarter-finals sin Spain would feel weird.
The newspaper made a game attempt at consolation: "Don't cry. We'll have a team and we'll be back." Back then, they were just another fan group that had to hand it to Zidane.
Only an older Spaniard or a world-class memory could reel off France in 2006 (round of 16), South Korea and the disallowed goals at Gwangju in 2002 (quarter-finals), third in the group behind Nigeria and Paraguay in 1998, Italy and Roberto Baggio in 1994 (quarterfinals) or Yugoslavia 2-1 in 1990 (round of 16).
Even fewer could go through third behind Portugal and Greece at Euro 2004, France in the quarter-finals of Euro 2000, England and the penalties at Wembley in the quarter-finals of Euro 1996.
Merely six years and one week on, a definition has changed about as thoroughly as one ever does.
There went red and yellow bouncing again, an idea so familiar that it has gone from fresh and energising, to pretty orthodoxy, to allegedly boring and then hurriedly back to exhilarating.
From midnight in a desert to various times most everywhere, even in a place without many Spaniards, you could see them again, football's reigning centrepiece and the leading question for Brazil 2014.
Will Spain be too old by then?