A clause is packaged as 거 ('the fact that...') and 맞다 asks or asserts that the packaging is correct. Almost every line here is a check aimed at someone else — 선물 받은 거 맞지?, 저희 아까 점심 먹은 거 맞죠? — where the speaker is fairly sure but wants confirmation. Do not read 맞다 as 'match'; here it means 'is right / is the case', and the -죠/-지 tag is what makes it a request for agreement rather than a statement.