Why I can't see the image on Mobile Steam?
Solution 1:
The last signficant update to the iOS Steam app was in 2015. Embedded images are a relatively new feature in Steam Chat -- they were added as part of the July 2018 Chat Update -- so the Steam app does not support this feature.
There is, however, a separate Steam Chat app which does support this functionality. Why this wasn't made part of the other Steam app is a question that I don't have an answer to.