Meaning of "primers IL-2" in a scientific article
From the description, yes, those primers are supposed to be specific for the IL-2 gene. The way they would be used would be on mRNA, not DNA, so you could use them to quantify the level of IL-2 transcription. However, there seems to be some glitch in there, because while the first sequence (5′-CAGCTGTTGCT GGACTTACAGG-3′) matches rat IL-2 mRNA starting at 120 in the sequence,  the second one (CACAGTTGATGGCTCATCATCG) does not match any IL-2; a BLAST search only turns up random and irrelevant matches.   

This may be an error in the paper (copying and pasting the wrong primer, which is extremely common, unfortunately); it may have been an error in design (someone used the wrong primer and got lucky results that seemed to match what they expect); or I may be doing something wrong, which I'm not going to try to troubleshoot any more than this.

(Edit, as @VonBeche points out in comments the reverse primer is almost a match at 398, with a one-nucleotide mismatch that screwed up my search -- possibly allelic variant, but equally possibly a mistake)