Actually, neither is fully correct, but the first one is more correct. I would punctuate thus: The custom was to call once for each kill; but this was Angry Face's first, and, in his excitement, he kept yelling. You want to separate the phrase "in his excitement" with a pair of commas (if you can delete a phrase without ruining the sense, you need a pair of commas or a pair of dashes).
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.