For a marriage to be valid, there are other requirements in addition to sex, but yes, having sex (normal intercourse and it also has to be consensual) is one of the requirements. While marriage is indissoluble once validly ratified and consummated, it can actually be dissolved still after a wedding but prior to consummation. It has not yet been completed at that point. Although, the couple must also be open to children, they do not necessarily need to have born them for the marriage to be valid.
As for who checks up on it, in typically no one. Practically I do not see how they could in general unless some controversy arose, such as one party claiming the marriage is not valid for one reason or another, or if some impediment is publicly known.
I suspect this is using some made up definition of "normal" (devised by celebate men who have no idea what marriage and sex are like) and not by kind of statistical data gathering.