According to Roman Catholicism, is a person required to fast?

Yes. "Binding" and "obligatory" mean exactly what it looks like: "are binding upon" means "apply to", and "obligatory" means "mandatory" or "compulsory."

From the Code of Canon Law:

1251 Abstinence from meat, or from some other food as determined by the Episcopal Conference, is to be observed on all Fridays, unless a solemnity should fall on a Friday. Abstinence and fasting are to be observed on Ash Wednesday and Good Friday.

1252 The law of abstinence binds those who have completed their fourteenth year. The law of fasting binds those who have attained their majority, until the beginning of their sixtieth year. Pastors of souls and parents are to ensure that even those who by reason of their age are not bound by the law of fasting and abstinence, are taught the true meaning of penance.

1253 The conference of bishops can determine more precisely the observance of fast and abstinence as well as substitute other forms of penance, especially works of charity and exercises of piety, in whole or in part, for abstinence and fast.

This means that a Catholic within the ages of 14/18 and 59 who does not practice abstinence on Fridays or does not fast on Holy Wednesday or Good Friday is guilty of violating Canon 1251.

However, you will find that Canon Law is rather forgiving in actually imposing penalties for violation of its canons, unless that lack of imposition were to constitute a scandal:

1399 In addition to the cases established here or in other laws, the external violation of a divine or canonical law can be punished by a just penalty only when the special gravity of the violation demands punishment and there is an urgent need to prevent or repair scandals.

That being said, attending Mass on Sunday is also an obligation:

1247 On Sundays and other holy days of obligation, the faithful are obliged to participate in the Mass.

Here we see "obliged" again, and not participating in Sunday Mass is thus a violation of a Canon. But beyond that, it is a sin against the Third Commandment (cf. Ex 20:8–10). Analogously, not fasting or not abstaining from meat when demanded is a sin against Temperance (the virtue of self-restraint or moderation, opposed to the deadly sin of Gluttony), as well as against Obedience to one's Bishop, who requests this Work of Mercy from his flock.

Sins, however, can be classified as mortal or venial; a mortal sin rejects sanctifying grace and binds a soul to damnation, unless confessed, but a venial one, though it impedes the communion of a soul with the Lord, doesn't condemn them. The difference between the two is that the former involves "a grave matter," according to Canons 1854 and following:

1854 Sins are rightly evaluated according to their gravity. the distinction between mortal and venial sin, already evident in Scripture,^{Cf. I Jn 16–17} became part of the tradition of the Church. It is corroborated by human experience.

1857 For a sin to be mortal, three conditions must together be met: "Mortal sin is sin whose object is grave matter and which is also committed with full knowledge and deliberate consent."^{Reconciliatio et Paenitentia 17 #12}

1858 Grave matter is specified by the Ten Commandments, corresponding to the answer of Jesus to the rich young man: "Do not kill, Do not commit adultery, Do not steal, Do not bear false witness, Do not defraud, Honor your father and your mother."^{Mk 10:19} The gravity of sins is more or less great: murder is graver than theft. One must also take into account who is wronged: violence against parents is in itself graver than violence against a stranger.

Because the Decalogue does not mandate fasting, I would be tempted to say that the sin of neglecting abstinence and fasting is venial, but I disclaim that my opinion here should be taken as authoritative. In doubt, it's best to consult one's spiritual director. Of course, we must strive to avoid even venial sins, so the possible venial character of neglect of abstinence and fast should not be taken as a license to ignore it.

In summary, while there is no canonical sanction against failing to uphold this obligation, it is still a violation of a Canon, as well as a sin. While it probably does not impede Holy Communion, it is still something we should try to avoid if we can and confess if we cannot.