I find MatThePhat summarizes the concern at the heart of this thread the best. Though it is not what GustavAdolf intended, this concern is real for me.
"If Egypt is influential to everyone and me but Greece, what's to stop Greece's elimination from deciding the game 'out of nowhere'?"
I thought about it and I believe there is little cause for worry, as I hope to justify in this post. A few points to start:
Assumption: Sources of tourism all also generate culture.
Result: A civ's tourism is always less than its own culture.
Result: A civ that "dominates" another, toward the culture victory, exceeds that civ in culture (as well as tourism over culture)
Result: There is a well ordering of cultural power in civs. Anything can happen, but there is no ambiguity as to whose got the math on their side at the present rate.
Now suppose you are aiming for something other than a cultural victory, so your attention is not on the tourism bar all the time. Either you are coming close to cultural domination by one or more other civs, or you are not. If you're not, then keep it that way, no culture victory for Egypt. It's on you. If you are... you have some tough choices to make. It's your penalty for lagging culture.
On the flipside of your penalty, does the eminent civ player get a boon for boosting his tourism over these other players but not that last one? Wrong question. He is still a frenemy. Yet, he need only regard the remaining cultural holdout as his last threat, except to the extent you all want to war him. If the cultural holdout has comparative tourism, you have a game of
Civilization on your hands - two runaways** the other civs cannot allow to succumb to the other, but must individually surpass, all while not being destroyed by each other. If the holdout has only defensive culture, this situation is, thankfully, impossible, because we know:
Fact: Large cultural yields will only be possible from Great works and Artifacts (culture building bonuses lowered), i.e., tourism sources.
Result: Cultural defenses large enough to survive tourism imply the presence of significant tourism. (*except for EXTREME late-found civs, but no map makes this possible)
It takes two civs to have this situation, and it's symmetric (except one of them is doing better, of course!) Egypt and Greece must both be tourist powers, and they've been cultivating it all game, and this makes a situation no different from
Civilization in general, except for one worry. The central worry, given by MatThePhat, is how able are the "little civs" to pop the game, by destroying the Greece/Egypt even though they are dominated by the other, and will lose?
Will the cultural victory enable Kingmakers?
So I went into a proof about why it would not happen, and I was confusing the cultural influence systems with the ideological pressure systems.
We must hope that to the extent the cultural victory's exact rules present a threat of just such an endgame (or midgame?) scenario, they also impede, and slow, the ability of those influenced civs to carry out military conquest, on either a scale of eliminating an entire player, or of destroying his cultural defenses and giving the other player the game (including looting or razing his cultural buildings/great works). Of the first case, the inherent difficulty of a "complete kill" may need no assistance, but cultural assassination must be something the other civs, not to mention that rival cultural leader itself, can act to prevent in a reasonable timeframe.
I think the system is policed by the game's existing nature. If the endgame occurs, it is via the cultural eminence of one player, the failure to defend of another, the dominant military power of one player, aided by the first, but against all detractors, and the complete loss of the cultural race to that first player of everyone else. Victory was decided by players with power over those who faltered, no kingmaker.
**Culture is not a runaway like science. As far as we know, going to 100% influence does not remove your ability to build up culture and dig out, even to 99%, where you deny the cultural victory (and less ambiguously become public friend #1 of everyone else.) Second, the Apollo ship is a finish line, but culture is a moving finish line that you control, while great works and artifacts can be lost. And even if matching culture is futile overall, it doesn't tie into -everything- like science does.