special relativity - Is energy content of a system different depending on the observer?

For the sake of simplicity, let's imagine that the entire universe is empty except for a single lump of (classical) matter with mass $m$. In its center of momentum frame, it is clear that the total energy is simply $E_\text{CoM}=mc^2$. However, in a frame moving relative to it with speed $v$, we have $E_\text{moving}=\sqrt{m^2c^4+p^2c^2}> mc^2$ for all nonzero $v$.

Are we to infer that the energy content of a system can be different relative to the observer? Does this not violate the first law of thermodynamics?