TL;DR Your bag should be fine to carry based on the picture and the link you posted. The zipper should not be an issue as long as it's easy to open and the material fits inside comfortably.
The rules are fairly well defined but vary slightly from place to place. On a general basis, I would recommend carrying a transparent, resealable, plastic bag with a size no greater that 1 quart or 1 liter and dimensions when flattened to be lesser than 20cm x 20cm.
This is fairly clearly mentioned on the airport websites or the embassy websites.
For instance, the Gov.UK website mentions,
- containers should be in a single, transparent, resealable plastic bag, which holds no more than a litre and measures approximately 20cm x 20cm
- contents must fit comfortably inside the bag so it can be sealed
- the bag must not be knotted or tied at the top
Whereas the TSA website for US regulations mentions,
3-1-1 for carry-ons. Liquids, gels, aerosols, creams and pastes must be 3.4 ounces (100ml) or less per container; must be in 1 quart-sized, clear, plastic, zip-top bag; 1 bag per passenger placed in screening bin. The bag limits the total liquid volume each traveler can bring.
The Narita Airport, Japan website adds that if you don't have a plastic bag, you cannot carry liquids.
Store liquid in containers with capacities not greater than 100 ml (g), and place the containers so that they fit comfortably in a transparent resealable plastic bag with a capacity of not more than 1 liter. Even if a container measures less than 100 ml, it cannot be brought on board if it is not placed in the plastic bag.