Hello Chris,
I have this SQL query that might be relevant for what you are trying to do- if nothing else I think it will allow you to modify it depending upon if you're interested in associated domains and if domains are used in conjunction with subtypes (looks like they are from your screenshot). As you suggested- subtypes and domains are largely managed / stored within the gdb_items and gdb_itemtypes tables (if your geodatabase is dbo schema just change table owner schema from sde. to dbo.- the rest should work as is):
SELECT distinct
st.SubtypeCode,
st.SubtypeName,
st.DomainName,
dom.DomainCode,
dom.DomainValue
FROM
(SELECT
subtype.value('SubtypeCode[1]', 'nvarchar(max)') AS "SubtypeCode",
subtype.value('SubtypeName[1]', 'nvarchar(max)') AS "SubtypeName",
subtype.value('descendant::DomainName[1]', 'nvarchar(max)') AS "DomainName"
FROM
dbo.GDB_ITEMS AS items INNER JOIN dbo.GDB_ITEMTYPES AS itemtypes ON
items.Type = itemtypes.UUID
CROSS APPLY
items.Definition.nodes('//Subtypes/Subtype') AS Subtypes(subtype)) st INNER JOIN
(SELECT items.Name,
codedValue.value('Code[1]', 'nvarchar(max)') AS "DomainCode",
codedValue.value('Name[1]', 'nvarchar(max)') AS "DomainValue"
FROM
dbo.GDB_ITEMS AS items INNER JOIN dbo.GDB_ITEMTYPES AS itemtypes
ON items.Type = itemtypes.UUID
CROSS APPLY
items.Definition.nodes ('//CodedValues/CodedValue') AS CodedValues(codedValue)) dom ON st.DomainName = dom.Name
