In all honesty, I love that.
Is there any chance she's balancing the total lack of Montessori competition with additional competitiveness at home? It reminds me of an old SNL sketch where a manager is so annoyed by the slow drawl of his boss that he demands that all his subordinates speak like auctioneers to compensate. I'd be curious to hear her teachers' feedback.
Maybe the initiative behind the competitiveness is praiseworthy on its own. Framing can be a wonderful tool. It might help balance out her tendencies (if you're concerned) if you can redirect some of the external competition to internal competition geared around effort and outcome jointly.
A statement like, "It's wonderful to see you so excited to read! I love reading with you. Can you read farther ahead/a harder book than yesterday?" might shift the locus of competition inward at times. Giraffe could be a straw man if ever she gets frustrated with harder material.
Your daughter sounds adorable! I'm a bit bloodthirsty myself.
