I don't think it's appropriate to link to that page from here but go to the search results linked about and click the result I've mentioned, you can view the source yourself and maybe find something that I missed?
moopy... thanks for paying attention to the spirit of our linking guidelines. You're right that it would not be appropriate to deep-link to those particular sites. We also normally don't allow discussion of specific sites, search terms, etc, in our public forum, unless that's the only way we can explore a topic of legitimate general interest without stepping on anybody's toes.
Since this is a new search feature that I don't believe has been reported before... it was decided to make an exception to our general posting policy by allowing your link to specific serps. The whole point of allowing you to post these, though, was to have a discussion and explore what's going on, not simply to magically answer your question on the first try. Things are rarely that simple.
I'm going to take a chance and cite some of the specifics I see in the serp posted, before they change, and which go beyond just the question of structured data. I trust my specifics, which I think will be helpful, are not going to affect the competitive landscape of the results posted, which are in a language other than English.
I'm not happy, though, that any domain names have been mentioned. Let's keep them out of further discussion.
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This is what I'm seeing after looking around a bit... First, for the record, your query and the results were on Google.com, and they are in Hebrew, which makes some aspects of the situation difficult to explore for many of us who are restricted to English. I initially checked out your query in Google Translate, where the English translation is...
amsterdam deals A search for this query in any language would be extremely unlikely to return actual sitelinks, of the kind we've come to expect when we search, say, for a site by its brand-name.
The results do display multiple navigable links that link into the site, below the main listing... and I'd describe them as "sitelink-like", or "similar to sitelinks". They appear to contain information related to the input/output fields of the booking engines on the pages that display them.
Your serps example showed 100 results, and I saw pages having these deep links on only two of the results returned, one on a domain that's been named, which was very close to the top, and another on a domain that we might as well not name, which ranked at about #70.
These deep links were in groups of three links, in a column below the search description. The anchor text, in Hebrew, translated to results like these....
Dec 16 - Dec 19 - Amsterdam vacation package - $642
Dec 16 - Dec 21 - Amsterdam vacation package - $xxx
Dec 25 - Dec 28 - Deal Amersterdam - $xxx
And, on the second ranking site...
Wed, Dec 7 - Charter flight to Amsterdam
Wed, Dec 7 - Amsterdam vacation package
Thur, Dec 8 - Charter flight to Amsterdam
There were no prices on this second set.
Is Google returning javascript form output? The sites are different, as they offer different sets of choices... but the results from each are similar in this respect... that they are booking pages with sets of sample or "promotional" results on the booking form page. On the main page returned by Google via the link above the description, you'll find a grid of about 8 promotional results, each in its own div, representing summarized examples of booking form inputs and outputs.
Clicking on either an "Order" button on any of those promotional results, or clicking on the external "sitelink-like" links returned, will take you to a state of the booking form that you can then explore further.
Note that the names returned like "Charter flight..." or "Amsterdam vacation package" correspond to radio button settings on the search forms and to corresponding examples posted in the grid, which strongly suggests to me that what Google is indexing might be related to Google directly spidering the javascript booking forms... or at least indexing specific states of these forms intended to be indexed.
I'll stop here at discussing specific search strings that might be found in the URL codes. We shouldn't be posting those publicly, as searches on these seem to lead to specific sites using them. But apparently these promotional results are something that are Google-friendly enough that Google is testing them out.
This could well be a demonstration of Google's ability to index javascript that it can find via the booking form. Also, I should add that in my brief explorations, not all of the external links are Promotional examples that were simultaneously visible on those main pages... but they all appear to come from booking engine output.
Additionally, I cannot find any evidence of schema or of JSON-LD on the pages. Remembering back to when Google tested every conceivable different way of entering and exploring a site, this could well be a limited test of another variant. I can see in travel where it would be extremely productive.
I should note, btw, that I could not duplicate these results in English on a variety of Google.tlds, so this test, for a variety of reasons, might be confined to Hebrew sites only for now.
I did see other sites for this query that displayed featured results on a page, but didn't have time to explore the code or see why they were not selected. Again, note that the second result that returned these extra links was at roughly position #70, so it's not a question of top pages only being awarded this feature.
I myself would appreciate deeper insights into what makes this work, without getting into specifics of the CMS or module used in these sites to produce these results. I'll leave it to other mods to jump in about whether this is getting overly restrictive, or revealing too much... but I can see where getting too specific might disrupt a whole niche. Hoping this helps further exploration.
PS: Edited to make changes in moderator's notes above and in some details of my post to clarify.