Based on the product you linked and your aversion to "bedside computers", I selected alarms with a similar rear-projection type display.
Echo Dot (3rd gen) with clock - $45
Luckily for you, Amazon has an upcoming version of the Alexa-equipped Echo Dot that meets all the requirements. It's got a dimmable display, all the normal Alexa bells and whistles (...
The Zettaly Avy seems to be a good option, though I'm not sure if this is still in your "cheap" range.
It has a full Android tablet, pretty up-to-date with Android 6.0 (not the latest...but not that bad either) and comes with the Google Play Store.
Here On Amazon for $129.99
An additional recommendation: the Cubie series of bedside clocks; there are at least four models (listed under "Cubi") on Amazon. My spouse has one and its display is somewhat dim; it autosets time (somehow) and has USB charging ports. Be advised that its idea of "now" and yours might differ: hers is consistently three minutes behind the time our smartphones ...