It looks like they have designed the page to prevent assistive technology like Kee from working correctly. Specifically, they rely on Javascript for form submission and have split each form field into entirely separate forms.
The latter reason is why you see only one field detected - Kee will actually find both but has to decide which form is the actual sign-in form and pick just one to fill your data into (and that’s the one where it will position the Kee icons into each field in the form).
By adjusting the form field configuration in the entry and probably also the whitelist, you should be able to get Kee to pick the form containing the ID field instead but I don’t think that will be all that helpful since the password field will then no longer work.
Are you sure that Kee fills the ID into the password field? I would expect that this part would work correctly, although only until the page’s own Javascript might try to break things.
If you’re not in an environment where you’re comfortable having the webpage remember your user ID, I’d suggest copy/pasting that into the correct field first and then if you ask Kee to fill the password field, it should work. Although again, their Javascript may mean that you will have to disable the auto-submit feature and click the button yourself.
By the way, for any future problematic sites enabling debug logging will give you more clues about what is going on with a particular page and might save some time spent through trial and error.