First of all, I want to state that current documentation indeed has mixed messages on the topic.
In the end, my understanding is - if you want a successful memory dump, it is not recommended to have a dump file without a page file.
The only fact we have is: the OS states explicitly that any memory dump is not guaranteed to contain complete information without a page file. This message appears for any type of memory dump while having no page file set in Settings - System - About - [Advanced system settings]
Windows might not be able to record details that could help identify system errors because your current paging file is disabled or less than XXX megabytes.
Also there is a statement that implies you must have a page file in article Configure system failure and recovery options in Windows
To take advantage of the dump file feature, your paging file must be
on the boot volume. If you've moved the paging file to another volume,
you must move it back to the boot volume before you use this feature.
Though it is not 100% clear if this statement refers to all dump file options, or only to the last one mentioned in the article.
Also, in the same article, all options state explicitly you must have a page file (except the last one)
- Complete memory dump
[...] you must have a paging file on the boot volume [...]
- Kernel memory dump
[...] you must have a pagefile large enough to accommodate your kernel memory [...]
- Small memory dump (64 KB)
[...] this option requires a paging file of at least 2 MB on the boot volume [...]
- Automatic memory dump
[...] contains the same information as a Kernel Memory Dump [...] Windows sets the size of the system paging file [...]
- Active Memory Dump (implies indirectly)
[...] Active Memory Dump is similar to a Complete Memory Dump [...]
So it seems, you can still configure the dump file without a page file set, but it is not guaranteed to contain all the data necessary for debugging.
As for configuration itself, all commands are outlined in the article Configure memory dump files for Server Core installation