Welcome to the forum...
Your booktype has indeed been successfully set to DVD-ROM. (and as such, I have changed the thread title to make it less misleading)
Some things to consider:
1/ Some old drives may not be able to read RW media correctly, regardless of booktype.
2/ Some drives may read WORSE with the DVD-ROM booktype. You should booktype a DVD+RW burn only if using the DVD+RW booktype causes problems. My LSC-24082K combo drive struggles every time it reads a +RW booktyped to -ROM, but not when it reads an unbooktyped +RW. If you haven't tried reading the disc with just a +RW booktype, use the "Write Now" button to change the booktype back to +RW and try again.
3/ This could also be caused by poor burn quality. [thread=119042]Posting a KProbe scan[/thread] may be helpful...