Why are some airlines omitted from GDS listings?

The reason is likely because they decided not to.

Adding an airline to the GDS (actually to several GDS) is not a simple process, as the airline's reservation system needs to communicate with each of the GDS in real time, showing all inventory, allowing blocking of seats, fare mixing and building, special requests, etc.

The airline needs to be part of the IATA / ARC payment systems so that bookings through the GDS by travel agents and other sources can have financial matters, such as refunds or payments, processed and monitored.

For a tiny airline that can be a huge financial commitment.

Why do you see some small airlines? Perhaps because they have contracted with one of the GDS to provide their in-house reservation system. GDS players like Amadeus offer turnkey airline reservation systems for start up or smaller airlines (there may even be bigger carriers who use these turnkey systems as well). And if you are using one of these systems you are already integrated into at least one of the GDS (probably all the major ones, as Amadeus would have to be competitive against other turnkey systems from the other GDS).

Although I cannot seem to find independent confirmation, I am almost certain ITA also sources its data directly from OAG and ATPCO, rather than relying on any GDS. At least, I think this likely in the years since their acquisition by Google.

Airlines don't provide their information directly to GDS companies. There's an additional layer, largely hidden from the public, which handles distribution of fare and schedule information.

Most major airlines submit their schedules to a company called OAG, previously the Official Aviation Guide Company, which has published combined airline schedules in one form or another since 1929. The airline doesn't need to share all of its flight information, only that which is useful to distribute to OAG's customers.

Fares, on the other hand, are filed with a company called the Airline Tariff Publishing Company (ATPCO), which began as a project of the ATA (now known as Airlines for America) and was spun off as an independent entity in the 1960s. Again, an airline doesn't necessarily have to file all their fares with ATPCO, only those which they want distributed to ATPCO's customers.

OAG and ATPCO then process and package all of this data in consumable form and sell it to GDS companies, airports, ground service companies, aviation consultancies, and anyone else who wants to pay for it. GDS companies (and ITA) then provide mechanisms for searching and booking, mixed and matched with yet other data from the airlines, from OAG, and so on about seating inventory, flight status, and so forth, and sell access to these systems to travel agencies.

Now let us take your example of WRY-PPW. A direct Google search turns up the schedule just fine:

^{Valid through Nov 13, 2017}

But if I follow the "search flight prices" link, Google tells me "Prices are not available for: Loganair" and therefore it can neither display them nor book them. As I am not privy to ITA Software's various business relationships, I will need to engage in some speculations:

1. Perhaps Loganair has not provided the fare information to ATPCO
2. Perhaps Loganair submitted fares, but ATPCO has not packaged the information in a way that Google Flights can understand it
3. Perhaps Loganair did not submit its own fares, but only sold those seats as Flybe seats, so when the two airlines terminated their contract, those fares were invalidated.

Now, the original question asks why small airlines and low-volume flights can be found in some parts of the world and not in others, and to that— again speculating as we do not have access to all the business decisions of all the airlines— market history and market pressures are likely to blame. The U.S., for example, is a very large market for air travel, with well-developed travel industry infrastructure. A small airline might well find it worth the effort to file their fare and schedule information so that they get "seen" by travel agents, especially if their competitors are doing so. Or, they might submit their fare and schedule information to one particular provider, as a small airline is likely to outsource its reservations system rather than develop and maintain their own in-house.

In other parts of the world, an airline might not derive many sales through GDS bookings. Low-cost carriers in developing countries, in particular, may get most of their bookings from direct sales through ticket offices or their websites. If so, the infrastructure necessary to submit fare and schedule information may simply not be worth the effort.