Middleware is considerably more difficult to determine compared to other article elements. It's normally not something a developer will highlight when selling the game, so don't expect to find good information purely through stores and official websites. The best way to figure out what 3rd party middleware a game uses is to dig around in the game's file system and find DLL files that are associated with such middleware. The Editing guide has a small set of tables denoting all the known DLL files that are associated with a particular middleware.
If you want something more automated, you can try a process monitoring program like the official-ish Process Explorer or 3rd party API Monitor, both which give you a list of all the DLLs a running process is using at that moment. Just keep in mind that some process monitoring programs (especially free ones) may contain malware.
However, before doing all that, check the game intro videos, credits, and manual (if available) for middleware details first. Most of the time, they give a complete or almost complete list of what was used.
In any case, some level of original research will need to be done on your end to make that association.
On another note, your API table entries for both games had some lacking details/minor inconsistencies (which I've corrected):
- The API and Middleware tables go under the "Other information" subsection. The editor templates don't auto-generate this header, so keep that in mind.
- If a game uses no 3rd party middleware, the Middleware table can be omitted from the article.
- You don't need to denote the exact version number of DirectX 9. That can be delegated to the System requirements table. Only list the major version used (ex. 9.0c -> 9).
- For the Shader model field, you can drop the ".0" suffix and write just the major version. I personally find it redundant, especially with games that use multiple Shader models.
- For multiplatform games, the APIs used across all versions need to be noted (the Windows release uses DirectX, while the OS X and Linux releases use OpenGL). Even if the exact version of OpenGL is not known, putting in a ballpark equivalent based on the DirectX versions (see the Editing guide for details) used or even just "Unknown" is fine.
- If a game is 3D and uses DirectX, the Shader models used need to be noted. Thankfully, unless otherwise stated, the specific version used can be denoted based on the DirectX version (again, see the Editing guide for details).
I hope all of this helps. And keep up the good work with those edits. Aside from minor issues, they are all generally high quality. I'll take a look at the other completed games you noted when I got the time later on.
One final note: please post all future completed games to this thread. The other thread you were replying to (Part 4) has been archived for some time now. Going forward, I will ignore all further posts/edits made in the archived thread.