Why does Instant Runoff lead to 2-party domination, while (delayed) Top-Two Runoff leads to multiparties?

We don't completely know why. But here are some factors that probably have something to do with the answer. Probably the first and last ones are the major reason, but the middle ones are at least related.

Instant Runoff (IRV) Top-two runoff (T2R)
In a 3-candidate IRV election, if voters strategically rank the two major-party candidates top and bottom to try to maximize their vote's impact (and we claim real world voters will do that a lot of the time, no matter how many IRV advocates tell them not to; 80-95% of Australian IRV voters exhibit this sort of behavior) then theorem: the same winner will be elected as strategic voters ("always vote for a major-party candidate so as not to waste my vote") would have elected under plain old plurality voting. This is a major defect in IRV and a big reason IRV leads (experimentally), just like plurality voting, to 2-party domination. With T2R in a 3-candidate election, strategic voters will not necessarily elect the same winner as the strategic-voter plain-plurality-voting winner. (Because of the second round, featuring honest voting only.) This is a major success of T2R and a big part of the reason it experimentally (in the countries in which T2R is used) leads to multiparties and avoids 2-party domination.
    It is a fact that the "flip rate" of T2R winners away from plain-plurality winners is over 3 times IRV's flip rate.
Good IRV voter strategy can involve dishonesty about pair-comparisons occurring in every IRV round. Often, it is strategically good to "betray" your favorite third-party candidate by not voting him top. In contrast, in top-two runoff, voting for the third-party true favorite usually won't hurt you in the first round, since that way he may make it to the second round and the honesty of voters in that second round may suffice to elect him; whereas if he fails to make it, then usually the major-party candidates will make it and you'll still have the opportunity to vote honestly on them next round. Good T2R voter strategy is always to be honest in the second (final) round. However, T2R voters might reasonably choose to be dishonest in the first round by intentionally voting for somebody horrible: If it's A versus B versus C with the other candidates D,E,... unlikely to make it into the second round; you want A and are fairly confident A is going to be in first-place in the initial round; and you are fairly confident either B or A would beat the horrible C in a head-to-head runoff; then your best strategy is to vote C.
IRV can involve a very large number of rounds. T2R only involves 2 rounds. So the two are not equivalent even for "honest" voters. (Also a different set of voters might participate in the second round, another kind of inequivalence.)
IRV elects a winner different from the plain plurality winner about 5.8% of the time, but T2R differs from plurality about 16% of the time. (And, of course, plain plurality is well known to yield 2-party domination.) With T2R, Prof. Steven J. Brams speculates that the "underdog effect" may be the reason more plurality-winners are overturned by the runoff. ("Underdog effect" = "The desire to vote for an expected loser.") Brams refers to chapter 3 of his book Paradoxes in politics: an introduction to the nonobvious in political science (Free Press, 1976) for discussion.
With IRV, if the top two vote-getters from the first round include the Condorcet ("beats-all") winner, then there is no guarantee that he will be elected. He might be eliminated in the very next round. With T2R, if the top two vote-getters from the first round include the Condorcet ("beats-all") winner, then he is guaranteed to be elected.
In IRV, 2-party domination causes the media to focus mainly on the candidates from the two major parties, which reinforces... 2-party domination! In T2R countries, (a) the media often runs polls of the form "in a hypothetical 2-contender runoff between X and Y, who would you vote for?" which often generates media focus on good third-party candidates. And (b) if a third-party candidate does manage to make it into the second round, the media gives plenty of attention to both from then on, giving the third-party one an equal shot.

Let's explore an explicit numerical example

Suppose A and B are the major party candidates and C the third party. To avoid the possible IRV "C is spoiler" scenario voters who honestly favor C, instead strategically exaggerate to vote either A or B top (and the other one bottom), with C middle, in IRV. (Voters know from past experience that the IRV spoiler scenario occurs with probability considerably greater than the historical probability C will win – probability estimates – and here and here are typical IRV spoiler scenarios intended to be simple, whereas this one is intended to be realistic of the sort that arises in "1-dimensional politics.")

Suppose the electorate's honest votes would be

#voters their vote
16 C>A>B
17 C>B>A
35 A>C>B
32 B>C>A

where the bottom two lines are due to most A- or B-supporters viewing C as the "lesser evil," e.g. consider that C is a "centrist."

Then the strategic IRV votes are:

#voters their vote
51 A>C>B
49 B>C>A

And A wins. This illustrates the damning fact that with strategic voters (who act this way) in a 3-candidate election, the IRV winner is always the same as the plurality (strategic voter) winner.

(And no matter what IRV advocates say, I'll still believe based on my polling experience that a lot of voters are going to act this way. Believe it. It is reality.)

The top-2-runoff voters vote (in the first round):

#voters their vote
33 C
35 A
32 B

and then in the second round it is A versus C and of course strategic and honest voting are the same thing in this round, so

#voters their vote
65 C
35 A

And C wins hugely. This illustrates the fact that with strategic voters, 3-candidate IRV and T2R elections are not the same thing, and T2R can elect third-party candidates.

Of course in our analysis above, we were assuming the first-round T2R voters voted honestly. Thinking strategically, the A-supporters based on history figure the main threat is B. They will vote A, or conceivably (if they are convinced A is going to make it to the 2nd round regardless) they might vote C. Same reasoning reversed applies to the B-supporters. Finally, the C-supporters figure C has little chance but can only get a chance if they vote C; and if C does not make it to the second round, then fine with them, they'll be able to express their A versus B preference next round and haven't hurt themselves. All of these strategic considerations only make everything we just said more true – i.e. C will win even more.

This kind of scenario and voter thinking presumably happens often enough to account for the observed fact that IRV countries are 2-party dominated (in IRV seats) whereas T2R countries have multiparties.

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