There’s no law that you have use ribbing, though it will keep the glove on better. I have to admit that the ribbing on that glove doesn’t look all that great, so maybe with your yarn it would look better. Worth a shot.
Knitting will stretch by nature, including garter, but it won’t pull in and be as snug as ribbing. You can knit with a strand of elastic thread held together with your yarn and see how that works.
Garter stitch is pretty stretchy.
The purpose of ribbing isn’t really to make things stretchy – it’s to make a section of the sweater pull in (at the waist or wrists, for instance. You can omit the ribbing and just do the whole thing in garter. But it will change the look of the sweater, and it may look unfinished. You could finish the edges with a few rows of another stitch (seed stitch, maybe) or some i-cord.
ETA: Sorry, I didn’t look at the link so I didn’t know you were talking about a glove. Yeah, the elastic should work. Either do what Ingrid says and hold it along with the cuff stitches, or run a few rows of elastic through the cuff area when the glove is finished.
I’m in agreement with Ingrid-- that photo is either not so hot, or the ribbing just doesn’t look not so hot with that particular yarn. But it’s done 1 X 1, and you could do a 2 X 2 or 3 X 1, which a lot of people like-- as there is only 1 purl st to 3 knit sts, it looks the least ribby. There are plenty of other options for the cuffs of gloves, including cabled, or sideways ribbed-- that is, if it’s in the round, K 4 rows, purl 4 rows, until it’s the length you want. Check out www.knittingpatterncentral.com and their mittens and gloves section and see what you like.