If you're fine with the main body of the file containing allele counts (0/1/2) rather than allele names, you can use

plink --bfile data --extract snps.txt --recodeA

and then use Unix cut to remove any header columns you don't want.

Otherwise,

plink --bfile data --extract snps.txt --recode compound-genotypes

(this requires PLINK 1.9) will almost get you there, but you'll need to add a header line on your own. Or

plink --bfile data --extract snps.txt --recode

works if you want two columns per SNP.