Sorry I missed the part that you only posted column 7 from your file. Either use @dschika's solution below or cut the 7th column and then use the one liner below.

$ awk -F ";" '{sub(/gene_name/,""); print $4}' your_file

If you don't need the quotes around the gene name

$ awk -F ";" '{sub(/gene_name/,""); print $4}' your_file | sed 's/"//g'

Assuming the fields in your gtf are tab separated you could try something like this:

awk 'BEGIN{FS="\t"}{print $7}' YOURFILE | awk 'BEGIN{FS="gene_name"}{print $2}' | awk 'BEGIN{FS=";"}{print $1}' > OUTFILE

genomax2 solution with sub is nicer.