In this case, the only possible answer is that this type of data is discrete. This cannot possibly be continuous.
Continuous data must be able to have pretty much any value. Specifically, continuous data can come in fractions or decimals. This is why you can tell that this is not continuous data. There is no way that a kicker can kick 2.3 field goals in a specific game. If this were an average, okay, but not in one specific game.
Discrete data have only a finite possible set of outcomes. These are often set apart by intervals. In other words, in this case, the answers can only be in whole numbers so the possible answers are finite and have intervals between them.
Please refer to the link for more examples.
In statistics discrete data refers to data on variable that can occupy a limited number of values. Generally these values are whole numbers, such as numbers of students in a class, or number of days in a week. However in statistics it is possible to have discrete data contain fractions. For example, statistical data on time taken to complete a step in a manufacturing operation may be measured to an accuracy of nearest 1/10 the of a second. This kind of data will discrete because it will accept values like 3.6 and 3.7 seconds but not any value that lies between 3.6 and 3.7.
In case of continuous data there is no limitation about the number of possible values the data can take between any two given values. For example, in case of continuous variable the number of possible different time values between 3.6 and 3.7 seconds is infinite.
The data in this case is discrete as an item of data can only be a whole number. For example, there is nothing like a half or 0.3 goal made or scored.