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I ran across this article today about how moons might have moons. In Daniel Keys Moran's universe, an Earth-sized planet named November orbits a gas giant named Prometheus. November is inhabited, colonized by humans.

... The next time humans will make an attempt similar to this one is in the mid-twenty-second century Gregorian, a world that orbits a barely subsolar planet named Prometheus.

The world is November.

Would a water-bearing, Earth-sized moon orbiting a super-Jovian gas giant have tides from the pull of the parent planet, or would a moon be necessary to make that happen?

Depending on its distance from the planet, it would probably have such strong tides that it was tidally locked to the planet, and the tidal bulge stayed in one place all the time rather than moving round the moon like tides do on Earth. But if it wasn’t tidally locked it would certainly have tides, probably very strong ones. Tidal strength varies with the mass of the tide-generating body and the cube of its distance, so you can calculate the strength relative to the tides created on Earth by the Moon yourself.

If it's not tidally locked, it will have tides.

On Earth, the moon creates the tides, but the sun does also affect them. You can especially see it in action when a solar eclipse occurs, as both attraction forces combine to create a super tide.

In the case of a Jovian-like system, the parent planet will exert the same kind of attraction on liquids on its satellite. You could probably see it happen on Titan if it wasn't tidally locked to Saturn.

In my Astronomy class when discussing tides my professor emphasized the tidal forces acted upon earth are equally acted upon the moon it's just so disproportionate the our moon has become tidally locked. On other moons this is not the case, but you should know that it is not uncommon for a moon to be so.

Another thing you might want to take notice of is that this status changes over time. tidal forces slow down the periodicity of an orbiting objects rotation which is how celestial bodies eventually become tidally locked, or slow to such a degree that a single "day" takes over a "year".