They are talking about schema here....and schema is a massive (and sometimes complicated and often misunderstood) subject (especially for someone completely new to it).
So, what I will say here is
very high level and the strong advice would be to really study it in (more) depth to get to understand it properly. It would be impossible to cover all the nuances of the subject here, but there is a lot of info online (some of it very good, some of it OK, some of it misleading)
"Google supports three different formats of in-page markup: JSON-LD (recommended), Microdata, and RDFa. "
You have implemented JSON. Specifically 'Corporation' schema. (you can test it here........
https://validator.schema.org/ )
There are many types of schema. Most websites (in our industry and many others) would normally tend to use 'Organisation' schema instead of 'Corporation'. In fact, until now, I don't think I've seen anyone using 'Corporation' although no doubt there would be some. And....I'm making an assumption here that 'corporation' is an alternative option to 'organisation'. That seems logical to me but I would have to go read up to be absolutely sure.
Note, if I'm right, that does not
necessarily mean 'Corporation' schema would (or might) hurt you. From experience (and it's possible it's flawed experience, but I don't think so) if you get schema wrong or have an error in it in some way,
I believe it's just ignored rather than it impacts you negatively).
So schema can help in the ways described, yes. If implemented properly... as examples.......it could help get you the featured snippet position for a search term (position zero...but also note you could still get a featured snippet position - at least until recently -
without any schema) and/or it could show things like star ratings or FAQs off the page in the SERPs results.
So, the appearance/manifestation of those in the SERPs would/might clearly get you more visitors/clickthroughs.
But..........
1. the schema you have implemented won't help with either of those types of examples, you would need 'FAQ' or 'Review' schema (and/or one or more of many other types).
2. your page(s) won't necessarily rank (and therefore attract more traffic) just because schema is implemented (the content still needs to be high value/high quality).
3. Even an ultra high quality page may not rank higher just because it has valid schema.
4. Schema won't (
on all known evidence) improve the ranking of a page just by the fact of it being there.
So...those pages/sites used as examples are probably true, yes. But they would have done a lot more with their schema implementations than you have (so far).
Now...at a
site level (rather than a page level) schema does (or can do) other things that are beneficial. I won't go into that here..and even when you get to that stage, any beneficial outcomes are hard to actually quantify.
For your two sites specifically, at this stage, I would heavily suggest you focus more on building/improving/enhancing the content and overall structures. Sure, you could investigate schema deeper alongside that, and having (good) schema would be desirable, but (to be blunt) I don't think it will do you any good unless you have made those site improvements. In which case, you have to look at it as a 'balance of time/effort' exercise.......
Your best balance of time/effort (
right now) is to build up the sites and improve them (from a visible content perspective + implementing/overcoming various other forms of underlying format/structure improvements or fixes - if any are needed). If you can do that
and learn/build schema alongside then go for it. If you can't, then work on the other enhancements first.