It's fascinating that their memo dismisses their search position so easily, but focuses on graphs for shopping and travel that shows them in a weak position in those areas, as either the memo is hiding their real arguments (which might not be unreasonable - given its audience and the odds it would leak), or they have not thought this through.

What the graphs show is that there are a number of strong competitors in the shopping space, which may create a strong public interest in ensuring Google is not being allowed to use it's perceived search monopoly position to muscle into the space and limit competition by giving itself better positions in results.

If the EU Commission finds that Google has a sufficient near monopoly on search and that their practices with respect to expanding their reach in shopping is anti-competitive, then Google's current weak position in shopping is entirely irrelevant unless they're hoping to show that being given such a prominent position in their search results does not give a business any advantages (their ad sales people ought to start hyperventilating if Google makes that argument).

And in fact the existence of a healthy, competitive eco-system in shopping would make any anti-competitive behaviour by a powerful monopolist far more damaging and important to curtail in the eyes of the EU Commission. It should not be something you'd want to draw attention to.

A much better argument would be to highlight far more the breadth of niche search engines, and how e.g. searches on Amazon and Ebay and others should also be included in any assessment of search market share, and that this would show that Google's market power is not as great as it would seem if you only look at "general purpose" search engines.