Can any creature with the "elf" subtype (such as the third-party race Houri) qualify for character options which require the character to be an elf (such as the Breadth of Experience feat), or are such options limited to full-blooded elves (and creatures with the Elf Blood racial trait)?
This is an old question, but a frequent one and the other answers have missed a decisive rule from the Advanced Race Guide:
Every humanoid creature also has a subtype to match its race, such as human, giant, goblinoid, reptilian, or tengu. If you are making a new humanoid race, you should either find an existing subtype to match or make a new one by using the name of the race as the subtype. If you are making a halfbreed race, it should have the racial type of both parent races. For example, a half-elf has both the human and the elf subtypes. Subtypes are often important to qualify for other racial abilities and feats. If a humanoid has a racial subtype, it is considered a member of that race in the case of race prerequisites.
This passage from the race creation rules should settle matters conclusively. As for your example, since the Houri are Humanoids, they qualify for character options, that have "Elf" as a prerequisite.
This also renders the "Elf Blood" racial trait of Half-Elves moot, since they have the "Human" and "Elf" subtypes; the trait now only matters when a Half-Elf changes creature type to something other than Humanoid (e.g. Outsider as a 20th-level Monk).
The elf subtype includes...
elves and creatures related to elves
Creatures related to elves are not necessarily elves and would therefore not always meet the prerequisite for Breadth of Experience.
Prerequisites: Dwarf, elf, or gnome...
As you seem to recognize, Half-elves (and some other creatures) can meet these prequisites because of the Elf Blood trait...
Half-elves count as both elves and humans for any effect related to race.
...but without being a literal elf or having a trait like this, they do not.
Possibly not by RAW - but you probably want to rule affirmatively in some cases
There isn't a strictly a clear definition on what qualifies a creature as being a capital-E Elf, but we can extrapolate from what rules do exist.
The "elf" subtype itself is very simple, and states only that:
This subtype is applied to elves and creatures related to elves. Creatures with the elf subtype have low-light vision.
This allows for the possibility that a creature could be sufficiently related to elves to have the elf subtype but is not, strictly, an elf. You could thus read the rules to infer that the elf subtype is not enough to qualify the creature for character options that have a prerequisite of being an elf.
We can also look to examples like the Half-Elf:
Type: Half-elves are humanoid creatures with both the human and the elf subtypes.
Elf Blood: Half-elves count as both elves and humans for any effect related to race.
In this case the character may have the elf subtype, but it also has the explicit racial trait Elf Blood which means it is able to qualify for elf-only character options. It may be that it is considered to have the elf and human subtypes only because of this racial trait. Either way, it's an explicit feature which means the half-elf qualifies for things as if an elf, and it's separate from the creature simply possessing the subtype "elf". Rules-as-written, it looks like it's a trait like Elf Blood which qualifies a creature that is not-an-elf for elf-only options, and the subtype is incidental.
On the other hand, we're hardly talking about a core mechanical issue here. The question of whether or not someone counts as an elf does not come up very frequently, and ruling favourably for a character that wants to take an elf-only option is not unreasonable. Personally, I would adjudicate that anything with the elf subtype is elf enough to take elf-only options.
This seems like it's almost certainly an oversight for the Houri
In the third-party race you mention, as they are literally half-elf (and half-nymph), it would seem wildly unfair to not permit them to qualify for elf-only options as normal half-elves do. I would personally guess that the omission of a racial trait along the lines of Elf Blood which clarified the creature counts as an Elf and a Fey/Feyblood was accidental, possibly in the belief that having the subtypes was all that was necessary. Either way, I'd definitely rule that Houri are elf enough to take elf options.