*When I worked at a corporate firm in central London my best friend at work was originally from Ghana, so a black woman.
One day I came down to find her for lunch and she wasn't in her office. We had a new temp receptionist who I went to ask if she'd seen my friend.
I started to ask if she'd seen X.
She didn't know any names, 'what does she look like?'
The receptionist was black too and I found myself totally unable to say 'she's the black one' in case she found it racist.
'She's a lawyer. Dark hair, brown eyes, pretty, about my height, wears suits, funny laugh, ummmm...'
She gave me some serious side-eye. 'You mean the black one?'
My friend found it hilarious and since she regularly refers to the 'loud Scottish lady' or the 'French man with the odd hair' genuinely can't understand why liberal white people tie themselves into such knots to avoid using a descriptive word in an innocent setting.*
It is the setting which is key. In the example given above, telling the receptionist that her friend was black was useful in helping her to figure out who she was looking for.
99% of the time, when race/ethnicity/nationality is used, it is not a necessary descriptor.
From the OP's post, it does not sound like any descriptor was necessary at all. 'He was just such an angry man!' would have sufficed. Or, indeed even just 'He was just so angry!'. It doesn't sound like she needed any further info about how he looked, his size, his nationality, or any other descriptor as she has no need to be able to identify him in the future!
So adding 'little Indian man' to it, did indeed make it racist. It was an unnecessary addition.