As you said, '-mo' can be translated as 'also'. In the example conversation you wrote, however, it's showing the speaker's "unexpectedness". That is, the words which -mo is attached to weren't expected by the speaker. For example, in the sentence "だめだ。２まんもつかってしまったよ", the speaker didn't expect that he would use as much as 20.000 yen. Similarly, in the sentence "ぼくは３まんもまけてしまったよ", the speaker didn't expect that he would lose as much as 30.000 yen.
Whether -mo means 'also' or shows "unexpectedness" depends on the context. As far as the example conversation is concerned, -mo is showing the speaker's unexpectedness.
Hope this helps a bit.
Good luck with your language learning!