They are commonly sold as groundcovers, so spreading comes very naturally to them. OTOH, I have seen some that were pruned on a frequent enough basis to form softly mounding shrubs about 30-36" tall and as wide, if not wider. It will also grow almost vertically, if trained up the side of a house or wall/fence. Height is extremely variable :-))

My Emerald Gaiety climbed (12 feet) up the side of my garage.

IOW, it's climber.

But, if it has nothing to climb on ... ?

Yes: These cling like ivy and can grow fairly high up supports - the parent species actually has a sterile juvenile phase and a flowering and fruiting adult phase like those of ivy (Hedera). Variegated cultivars of wintercreeper show same or similar behavior. There used to be an Emerald 'n' Gold near here that had grown up the trunk of a Pinus sylvestris; the yellow leaves of the Euonymus were rather nice with the bluish needles of the pine.

A friend has a 'Silver Queen' or similar white variegated form that has grown up the corner of his house, out of view to pop out a few feet farther up. It has had to grow around the corner at a right angle to appear where it has. Getting it out from under the seam is going to be a bother (otherwise its thickening stems may eventually do some damage).

I have some that have formed nice 2 foot mounds without any support. Some of the new growth tends to shoot straight up, and I snip off some of the stragglers. This is in a part to mostly sun exposure (I have them in two areas) in well-drained sandy loam with ample moisture. It may be the amount of light or other conditions (soil type, fertility, moisture) in your case that are causing more spread than height?

As with ivy growth is sideways until a support is encountered. It seems specimens located away from something to grow up onto may never develop a climbing habit.

I have a bunch of emerald gaiety that have been in for about 9 years, and they never get taller than about 8". They have no support, so as Bboy said above, the growth is sideways. I trim them to make them look like a decent, (very) low shrub, but I have not found them to grow in height, no matter what type of pruning I do.