Firstly, a disclaimer - I will ramble a bit here.
@pvnks starts to shed some light on this, but as you can tell it quickly becomes a complex subject. Especially when you are looking at parks from Paultons to SFMM.
To briefly touch back on what was said above - the principle designer role is key and with it comes a lot of responsibility (the role is more about ensuring safety throughout the lifetime of the project, but covers a lot of other aspects), but the specific term is unique to countries following a specific EU directive. In the UK, this is managed by the HSE (under the CDM Regulations Acts). Similar roles do exist in other jurisdictions, I'm just less familiar with their terminology.
I think it's important to highlight the difference between engineering responsibilities during design, and those during normal operation.
A coaster is, itself, just a sub-package within a larger construction process. Engineers from lots of disciplines will be involved in a highly technical manner from the outset. To name but a few:
- Geo-technical: for things like foundation requirements
- Structural: for things like foundation design and other structures on the site
- Services: for things like drainage/water/power
- Infrastructure: for things like roads/bridges/tunnels
Then there are all of the specialist engineers or designers from the ride companies, theming companies, effects companies, landscaping, etc.
All of this is to say that, the term 'engineer' when used here relates to those people who are undertaking technical design calculations and methodologies to design the ride. It is highly unlikely that any park in the world has people like this on their payroll all the time - there's little-to-no point. Plus, they're hellishly expensive.
The creative minds that come up with the concepts may form part of these teams, but could be employed by the park directly. Same with some of the project management responsibilities (keeping all these excitable engineers in check). Likely a bit of overlap here, and would be dependent on the size of the project and park/chain.
So what about the park's ride engineers that will operate/maintain the ride for all these years? If I was being picky (and depending on your jurisdiction, the local law would say the same), these people aren't necessarily engineers. They're skilled mechanics and technicians, for sure, but they don't have any ownership over the design of the ride. As part of the development of the project they would be consulted as experts on the maintenance aspects of the ride, especially on things that would relate to requirements that the rest of the international design team may not know. For example:
- Park policy is that we can't use A-frame ladders over 6ft, therefore if we need higher access we'll have to use a temporary scaffold or MEWP, so we'll need this to be factored into the design (level areas or demountable theming, etc).
- Our maintenance sheds are all in the south end of the park, so how are we meant to get the replacement wheel assemblies from there to the ride?
It's the kind of knowledge that no-one on the engineering team would have without specific guidance.
Parks like Paultons simply won't employ any of the design side of things. They may even contract out the creative and project management bits too, if they're small enough. They don't do projects often enough, or of a large enough scale, to justify keeping people like that on. They will have their own team of maintenance staff who'd be consulted during the project.
Parks like SFMM probably have some of the more creatives and management-type roles in house (or as part of the wider chain), but again I'd be very surprised if they had their own design engineers. As a chain, Six Flags can probably justify having a number of project managers in their head office.
Both sides will understand aspects of the others' work, but in the modern era of needing to be able to delineate roles and responsibilities during large projects, they're often left to their own expertise.
TLDR: The park's in-house 'engineers' are involved in providing their specialist knowledge of the park and it's operations, but are unlikely to be involved in much of the technical design aspects of a new ride.