What If the announcement for a Tenure-Track position in a research-intensive university does not request a research statement?
Yes, a three page letter of interest would not be abnormal in these circumstances. Please keep the font size large given that the faculty on search committees have aging eyes.

My guess is that they've gotten over 200 applications for a single position in previous years and are attempting to do a first cull before asking for more details and letters. They should be commended.