I believe the second variant is the correct one.
We were buffeted by the running terrified crowd.
The article 'the' refers to the noun 'crowd'.
If you say 'the terrified crowd running' the article would make 'running' a noun, which is wrong. The interpretation that 'running' is used as a postmodifying attribute to 'crowd' is also incorrect because unlike the participles concerned, involved, etc. (the question concerned, the people involved) 'running' doesn't function that way.
Except in the set-phrase 'two days (/...) running.'

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