Many of the older, older machines do not have a zig zag stitch. For most purposes that does not matter. Particularly when using things like nylon which does not stretch that much. However, fleece, spandex and other fabrics designed to stretch will break stitches like mad. There are ways to minimize this on a straight stitch machine.
When stitching such things as elastic and stretch fabrics, pull the fabric/elastic as you stitch it. Stretch that piece out to the degree you expect it to be stressed. Also use a longer than normal stitch length. That will pucker the stitches on the piece, but it should not significantly compromise the integrity of the stitch. Then when the fabric is stretched in use the stitches are not pulled beyond their breaking point.
All in all a zig zag is nice to have for stretch applications. Most gear, however is perfectly reasonable without a zig zag. There may or may not be after market attachments that can be used for old straight stitch machines.