Welcome to the forum.
The link you provided was to a very inexpensive watch. If I understand your question, you are asking if you need one for traveling by bicycle. A decent watch isn't a bad idea and can even be a training aid if it has a stopwatch, countdown timer, and/or split laps, but the one in the link honestly doesn't look like much. For just a few dollars more you could get a basic Casio sport watch at WalMart or other chain store that is water resistant and has time, date, and a stopwatch.
If you have the money and are serious about doing more than casual riding or basic commuting, then a cycling computer that mounts to the handlebars is a good investment. You can get into basic ones for around $30 with wireless models running around $50, about the cost of an medium quality sports watch. Even the basic ones tell you speed, distance (total and trip), elapsed time, top speed, and average speed.
Remember that "looks cool" is secondary to "works well".