It is rather easy to define:
1) participle should define the noun or noun phrase
2) verb functions together with noun. So, the subject (connection) goes together with the verb (is). Thus, eating and excelling at are not verbs.
3) here eating and excelling at function as gerund since they take up some part of the noun functionality. When I studied English grammar the teacher explained it like this: gerund is something in between the verb and noun, i.e. it has functionality of both.
I am not a grammar guru, tried to explain in my own terms
Hope it helps.