Rendering an entity the formatter way I have written a custom formatter for taxonomy term fields. Now I would like to expand the module and add a custom entity renderer to show the entity in the very same formatter-like way, using mostly the same code.

The reason I need it is that while theming Search API Views fields, I'm not given an option to format term reference as a field, but only as entity.

I thought I'd provide a custom entity view (via hook_entity_info_alter). But then, how do I provide the HTML output of the entity?
You can't render an entity like a field and vice versa. These are two entirely different things. However if you in a field loaded a related entity and rendered as a way of rendering the field, there could be some common ground.

That being said, your reason for asking this question doesn't really make sense. If you have a field on an entity and want to render the field. No matter how you render it, (through views, by viewing the entity etc.) you will have to use a field formatter to render that field.

Also regarding entities there is no common way of rendering them. The module defining them can render them any way it would like to and it's up to that module to make a way to render the entity. That being said, the entity API module does create some apis for doing this in a generic way, but that is not a part of Drupal 7 core.