The gemara is medayek from the mishna that for testimony of damage we require Jews. The question is, why is it different than any other testimony where only b'nei bris are believed? The Nemukei Yosef says it is brought agav the others in the mishna, but really not necessary. The Rosh says that we would think to believe non-jews in the realm of damages either because we want the nizuk to be compensated or we had a hava amina to believe goyim when a goy was the one who damaged, so the mishna needs to say that we only believe jewish witnesses. Yam shel shlomo says that since in their courts, they are believed, we can also believe them, so the mishna needs to say that a jewish court cannot take money even from a goy who was mazik unless there are Jewish witnesses.
The Rambam in his commentary on the mishna says that since damages primarily occur in areas where Jews aren't present such as around farms and the like, we would think that those who are generally around in these areas can be trusted to testify about the damage. The Rambam also indicates that this is the hava amina in the Yad Hachazaka (nizkei mamon 8:13):
אין הנזקין משתלמין וכו' אלא בראיה ברורה ובעדים הכשרים להעיד, שלא תאמר הואיל ואין מצויין באוריות הסוסים, וברפת הבקר, וגדרות הצאן אלא העבדים והרועים וכיוצ"ב, אם העידו שבהמה זו היא שהזיקה את זו שומעין להן וכו
The Terumas Hadeshen (353) was asked about 2 women who were fighting about their makom kavuah in the shul (obviously in the veiber shi'il), and one had 2 women who were willing to testify on her behalf, can their testimony be admitted into th court? He rules that since women are more frequently found in that area, their testimony may be accepted. He supports this from the gemara in kiddushin 73b that the midwife is believed about a be'chor, since it is usually a woman who is present at childbirth. Why then do we not believe pesulei eidus such as goyim and women in the context of damages based on the same logic? The Terumas Hadeshen explains that if we believe pesulei eidus in the context of damages we are afraid of people hiring them to extort money from others, but in circumstances which are not common and only occur once in a while, we can use the sevara that the rambam rejects to believe even pesulei eidus. See Yam shel shlomo (41) who quotes this and seems to agree fundamentally, but takes issue with ever believing non-jews for these things because - פיהם דבר שוא ומרמה
The Rama (Choshen Mishpat 35:14) says that me'ikar hadin those who are passul for eidus are not even believed in areas where kosher witnesses aren't common. However, there was a takanas kadmonim to believe women in areas where men are not frequently found or for things that men usually will not know (such as the clothes that a woman was wearing).