Show a piece of a Google Spreadsheet document on Andriod main screen
Many thanks to beeshyams. Here is a way to do what I wanted.

This app allows to parse chosen content from any web page and use it as a widget. In order to have a Spreadsheets document as a web page one can publish it (File → Publish to the web...). The cells of interest can be linked from another page of this document (or even from another document) using formulas like =Sheet1!A1 so that the page being published would only contain what is expected to appear on the widget.

For now the widget I produced looks poor but there are plenty of customization capabilities including regexps and CSS so probably I will be able to tweak it according to my likings.