As mentioned in the comments, I don't think the Tiferet Yisrael meant that these men believed in Torah and Hashem as a Jew would. After all, the fourth person he makes an example of, which you didn't in bring your quote, is Johann Reuchlin, who was a Catholic scholar. Rather, they believed in God and that what Christians call "the old testament" is divinely inspired (it would be hard to imagine the Tiferet Yisrael calling the Torah "Ha'brit Ha'yeshanah". That's not really something that was done then).
However, as Rabbi Jonathan Sacks and Rabbi Jay Kelman point out, the Tiferet Yisrael's emphasis here is on the idea that Hashem rewards all of those who are deserving of reward, regardless of faith. A non-Jew who does a great act will still be rewarded, even if they aren't Jewish, as the Tiferet Yisrael pointed out previously that non-Jews are not animals and therefore, worthy of Hashem's just judgement. And after that he explains that even if they didn't follow the halachot of non-Jews perfectly, because of the great things they did, they would still be deserving of reward:
"ואת"ל דאף אלו החסידים הנ"ל אע"ג שקיימו הז' מצות של בני נח, אפ"ה אין דינם כגרי תושב, מדלא קבלום בפני ג' חבירים. ובל"ז ג"כ אין מקבלין גרי תושב רק בזמן שהיובל נוהג. אפ"ה מדלא עשו מעשה עשו. יש להם חלעה"ב [כע"ז ד"י]"
"And if you wished to say that even these pious men that we mentioned above, though they kept the seven Noachide commandments, even then they aren't considered gerei toshav [Noachides], because they didn't take upon themselves these [commandments] before three Chaverim. And also, we do not accept gerei toshav except only when the Yovel is kept. Nevertheless, since they did not act in the way of Esau, they have a share in the world to come."1
Which begs the question, is "the way of Esav" a reference to Christianity or does it simply mean not doing immoral things?
The gemara in Avodah Zara 10a (which is what the Tiferet Yisrael is basing himself on) says:
"On another occasion, Antoninus said to Rabbi Yehuda HaNasi: Will I enter the World-to-Come? Rabbi Yehuda HaNasi said to him: Yes. Antoninus said to him: But isn’t it written: “And there shall not be any remaining of the house of Esau” (Obadiah 1:18)? Rabbi Yehuda HaNasi answered: The verse is stated with regard to those who perform actions similar to those of the wicked Esau, not to people like you."
From here it seems that "the way of Esav" means simply doing immoral things. Those non-Jews who do not follow the way of Esav - being immoral - and do great things instead (the flipside) will receive a share in The-World-To-Come (just like Antoninus).
1 Thank you to @JoelK for assisting with the translation.
