I admittedly don't know the specific history of these houses or whether the additions came before or after Denver's first 1925 zoning code. But judging by the "streamline moderne" style of the retail addition to the structure on the corner, I would guess these changes happened in the 1920s or 30s. If I remember my Denver history correctly, Colfax didn't really become the kind of seedy place you describe until the the late 1940s or 50s. By the 1950s, houses like these would have simply been demolished and replaced with a 🞵🞵🞵🞵🞵🞵 strip mall or gas station (which you also see plenty of along Colfax).
When I see those structures, I imagine something more like a neighborhood corner market, or perhaps a tailor or other kind of small shop (and yes, corner markets often sell cigarettes). They were likely added by the people who owned and lived in those houses and decided that their "front yard" was worth more to them as a place of business than as a landscaped space when automobiles started using the street and it became a busy, noisy place. Kind of like a modern "live-work" unit.
For the record - there are actually examples of this
exact same kind of thing on Tennyson St (notice the Sushi restaurant actually has a house behind the mid-century retail façade). Including a modern example at the corner of 39th and Tennyson that is home to a hip new Mexican restaurant.