gff files does not have gene_id or gene_name columns that you can subset with dplyr::select(), always check your data format. For your particular case your gff file looks like this:
head(ITAG4.1)
seqid source type start end score strand phase attributes
1 SL4.0ch00 maker gene 83863 84177 NA + <NA> ID=gene:Solyc00g160260.1;Name=Solyc00g160260.1
2 SL4.0ch00 maker mRNA 83863 84177 NA + <NA> ID=mRNA:Solyc00g160260.1.1;Parent=gene:Solyc00g160260.1;Name=Solyc00g160260.1.1;_aed=0.30;_eaed=0.59;_qi=0|0|0|1|0|0|2|0|100;Note=Homeobox leucine-zipper protein (AHRD V3.11 *-* tr|Q8H963|Q8H963_ZINVI)
3 SL4.0ch00 maker exon 83863 84043 NA + <NA> ID=exon:Solyc00g160260.1.1.1;Parent=mRNA:Solyc00g160260.1.1
4 SL4.0ch00 maker CDS 83863 84043 NA + 0 ID=CDS:Solyc00g160260.1.1.1;Parent=mRNA:Solyc00g160260.1.1
5 SL4.0ch00 maker exon 84056 84177 NA + <NA> ID=exon:Solyc00g160260.1.1.2;Parent=mRNA:Solyc00g160260.1.1
6 SL4.0ch00 maker CDS 84056 84177 NA + 2 ID=CDS:Solyc00g160260.1.1.2;Parent=mRNA:Solyc00g160260.1.1
So both your gene and transcript id information are stored in the last column, "attributes". I am not sure what you mean by "extract" in this case, you just want a list of gene names or transcripts names for example? In that case you can first filter your genes or transcripts (with the "type" variable) then use a regular expression to retrieve the attribute of choice you are interested in.