Hi - HbA1c has been in use for a while but was only formally adopted as the measure in 2010. Historically HbA1c was reported as a percentage - being the percentage of a particular haemoglobin protein that had become glycated - had had a glucose molecule attached to it. Most of the world now uses (according to Bilous and Donnelly, anyway) the IFCC mmol/mol, although it's clear this is not widely used in the USA and many UK doctors still quote HbA1c in percentages.
As it doesn't test blood glucose directly, HbA1c is a proxy measure that allows an estimate of the likely blood glucose levels over the past 3-4 months. It isn't perfect by any means and its limitations are well known.
Conveniently the DCCT %s align neatly with mmol/mol - 5.5% is 38, 6.0% is 42, 6.5% is 48mmol/mol which makes me ask questions about how and why some of the mmol/mol figures were selected for diagnostic purposes.
I had not heard of GMI before and the Handbook of Diabetes doesn't reference it at all. I can see why Dexcom are pushing it - it's essentially an advert for their product. I'm not convinced by the "no lab interference" argument at all.
GMI seems to be a calculated derivative of CGM measurements - which don't directly test blood glucose either. If the reported results above are accurate, it means (assuming in IFCC terms that 1% DCCT is roughly equal to 11mmol/mol) that nearly three quarters of the GMI results differ from HbA1c by a considerable amount - enough in over 20% of people to have you diagnosed as T2 when your BG is actually normal according to HbA1c, or vice versa.