If you take a look at this Then & Now photo, you can see the left hand side of the HMV shop and how it used to look in its Princes Theatre days:
By the 1920s, its glory days as a theatre were long over and it had become a cinema called the New Princes Theatre.
It finally closed sometime in the 1960s, when the ground floor frontage was ripped out and converted to a shop, the Maypole. Later, it became a Liptons supermarket (with a cafe on the first floor), then FarmFoods, then Lo-Cost. Finally, in 2004, the building was refurbished and a more sympathetic shopfront added when it became a branch of the HMV music retailer.
You can still see a domed ceiling through the first floor windows, if you look carefully. And I recall a member on the Llandudno forum saying that he once came across the old Princes Theatre sign dumped in a quarry up by Nant Y Gamar woods!