また雨が降っている。今日も野球をするのをあきらめよう
It’s raining again. I guess I’ll give up on playing baseball today too. [casual-volitional]
It’s verb nominalization to turn 野球をする from a verb to a noun. You may be used to seeing のが or のは, but really only の does the nominalization, so it can be used with を too.
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The “no” turns a verb into a noun -
“yakyuusuru” means “play baseball”
“yakyuusuruno” means “playing baseball”, which is exactly what you need in the sentence
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I’m reading “Let’s” instead of “I guess I’ll”
Volitional can also be used for making a decision for yourself as the translation does, but I don’t know the specifics.
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Ah, seem to have completely forgotten that one, cheers.
That would be the verb[よう] + と思う grammar if I remember right.