x <- c(1:3)
y <- c('"gene_biotype \"lincRNA\"; gene_id \"ENSG00000224818\"; gene_name \"RP11-134G8.8\"',
       '"gene_biotype \"processed_transcript\"; gene_id \"ENSG00000261067\"; gene_name \"RP11-264B17.3\"',
       '"gene_biotype \"processed_transcript\"; gene_id \"ENSG00000261067\"; gene_name \"RP11-264B17.3\"')
dat <- data.frame(x,y)
library(stringr)
dat$x <- str_extract(dat$y, '(?<=gene_id ")[^"]+')
dat