Are these attacks considered magical?
Bite. Melee Weapon Attack: +14 to hit, reach 15 ft., one target. Hit: 19 (2d10 + 8) piercing damage.
Claw. Melee Weapon Attack: +14 to hit, reach 10 ft., one target. Hit: 15 (2d6 + 8) slashing damage.
Tail. Melee Weapon Attack: +14 to hit, reach 20 ft., one target. Hit: 17 (2d8 + 8) bludgeoning damage.
Fire Breath. The dragon exhales fire in an 90-foot line that is 10 feet wide. Each creature in that line must make a DC 21 Dexterity saving throw, taking 56 (16d6) fire damage on a failed save, or half as much damage on a successful one.
Best Answer
No - monsters' attacks are not magical unless specifically stated by the stat block
In D&D 5e, monsters' weapon attacks are not considered magical unless specifically described as such by the stat block.
For example, the pit fiend stat block in the Monster Manual has the "Magic Weapons" trait that says to treat its attacks as magical:
It looks like the attacks you're asking about are from an ancient red dragon. The ancient red dragon's stat block says nothing about its attacks being magical, so you should treat them as nonmagical attacks.
Also see Wizards of the Coast's article "Rules Answers: February 2016", which explains that dragons' breath weapons are not considered magical, either.
But... aren't dragons supposed to be super magical?
Yes, the introduction to the Monster Manual says that "True dragons... are highly intelligent and have innate magic"... but look at it like this: your average party wizard is also very powerful, but that doesn't mean that she automatically gets to deal magical bludgeoning damage if she hits a kobold with her quarterstaff. Magic can manifest in a lot of ways other than in attack and damage types.