Great question. It made me look into it and I discovered why it is so. Yes, masculine words ending in ת are rare, but they do exist and I am sure you know some of them well from this course - בית (house), מוות (death), צוות (team), זית (olive) and so on. I also found two masculine words in this course ending in ות, one of which is תות (strawberry) and the other is שירות (service) which is, just like עימות, a verbal noun in the pi'el binyan. So, this ת is there because it's the third letter of the root and since pi'el verbal nouns are masculine and have the pattern xIxUx, it causes confusion thinking it's a feminine noun.
Yes, there is a verb לעמת (to contrast, to confront). Not sure how much it's used, but its verbal noun apparently is.
Here is a link where you can find other pi'el verbs whose third radical is ת - https://www.pealim.com/dict/?pos=verb&num-radicals=all&rf=%D7%AA&b=D&page=1 Apparently there are only a few of them, and I'm not sure how much they are used, but might be useful information to you or someone else.