He was probably just continuing with the Mass so as not to draw even more attention to the paramedics and the man in need. I am sure the man was feeling bad enough and he didn’t want to be any more embarassed by the Mass being halted for him. Also, the paramedics would probably prefer to just get in there, do what they need to do, and take him out instead of trying to check vitals with an audience of hundreds of people focused entirely on them.
One time during Mass at a very big cathedral a woman started sobbing during communion. It wasn’t some small cry over something. She was clearly VERY unhappy. Something was weighing very heavily on her. The priest didn’t stop. Instead, a deacon came up from the back of the church and asked if she needed to talk to someone. She nodded her head and he lead her to the back to see what was bothering her. The cathedral is very near to some big hospitals. My guess is that she had gone to Mass after visiting someone or just losing someone.
Of course, my next story isn’t anywhere near as serious, but my sister locked her knees while standing in Mass and fainted. She was an altar server in that Mass so she basically fainted in front of the entire church. I think the priest didn’t know what to do. He was in the middle of a prayer and all the sudden an altar server wiped out a few feet away from him! He looked over and you could tell he was probably trying to remember whether or not anyone covered the topic of unconscious altar servers in seminary. When he saw my mother and another woman run over to my sister and drag her away he looked relieved and kept going with the Mass. Honestly, what good would it do to stop the Mass? Someone else was already taking care of the issue.
Another time, the church was having its flooring redone and so Mass was being held in the school gym. It was the middle of summer and it was HOT so the doors had been left open for a bit of a breeze. The wide open doors were quite welcoming to a little lizard that decided to walk right into the middle of the altar area during the homily. The priest kept going but it was clear that the lizard scampering back and forth in front of the altar was distracting everyone, including him. During the offering a little elderly man decided to catch the lizard with one of the extra offering baskets. If he didn’t catch it then it was guaranteed that the little lizard would have been stepped on during Communion. Seeing as how it is a church run by Franciscans we can’t have little lizards being killed during Mass without an honest attempt to remove them.

The little elderly man crept up behind it and slammed the basket down. I think he assumed that everyone was preoccupied with passing the other baskets around so no one would notice his attempt at removing the lizard. The lizard took off and as he tried to go for it again he slipped and fell. Then he tried to stand up and catch it and he fell again. It was much more of a spectacle than he ever thought possible, but he was victorious and the lizard was removed from the Mass all before the gifts were brought up to the altar.
Things happen in Mass. I think the key is to just keep going. Chances are there is an usher or someone that will take care of whatever issues are going on around the priest.