(a) The gemara first understood the pasuk to mean Hash-m rejoices. This prompts the question - does Hash-m rejoice etc. How can the gemara in the end seemingly say the pasuk doesn't mean Hash-m rejoices, based on the dikduk, but that He causes others to rejoice?
(b) Secondly, the verb form yasis is used in Isaiah 62:5 which seems to be the source for the verse in Lecha Dodi that we sing at chasanas. There the sense seems to be that Hash-m Himself is rejoicing. (And that is how Artscroll translates it in the siddur and in Isaiah) Based on our gemara, in Isaiah it should have said Yasus with a vav. And if the word yasis can mean either He rejoices or He causes to rejoice, then the fact that the pasuk in Devorim didn't write yasus is no proof.
max weiman, st louis mo
(a) The CHIDA (Machzik Berachah, YD 87:14, cited by Maharsham here) answers both questions with the following assertion. 'Yasis' can either mean "is happy" or "makes happy." But Yasus means only "makes happy."
Thus, normally, the two terms are interchangeable. But in the verse that our Gemara is discussing, since the intent of the verse is unclear the Torah should have used the unmistakable term. That is to say, if the Torah meant to say that Hash-m Himself is happy it would have used the term "Yasus," for otherwise we would shy away from saying that Hash-m is happy when enemies are destroyed and prefer to translate it as "makes others happy."
Rav Yosef Chaim in Sefer BENAYAHU offers a similar explanation, but adds that there is another reason we would shy away from saying that Hash-m is happy when enemies are destroyed and prefer to translate it as "makes others happy." The reason is because Hash-m always gives a greater measure of good than He gives of bad (Sotah 14b), so how could He be "as happy to punish you as He was to reward you"? Since the Torah should have been more specific if it indeed meant that Hash-m Himself will be happy, we can infer that He will not be happy; He will just make others rejoice.
(b) The SHELAH in Parshas Balak adds that even when Yasis is used to mean make others happy - it also means that He is happy. Hash-m is happy when we suffer in this world if it allows us to attain higher levels of reward in the World to Come.
Best wishes,
Mordecai Kornfeld
Kollel Iyun Hadaf