You could, you know, read a little more, especially for physics that is outside your scope of study. Just the fact that the person in the article has a Nobel Prize should be enough for you to take a moment to google a little and learn about physics that you might simply not be aware of.

CPA with Ti-Sapphire produces photons that are optical (near-IR specifically, usually 800nm) but it is their interaction with matter, usually solid density matter that is how you achieve that causes such violent reactions, it is in the so-called "laser-plasma interaction," specifically that the material you shoot with ultra-short laser pulses is immediately ionized into a plasma and that light matter interaction leads to all sorts of energetic by-products, including (easily) MeV scale radiation. Now the radiation does not have necessarily good beam qualities, which is part of the current focus of research, but it does happen and it is easy to reach MeV scale.

A good example of how different this regime is that if you're sharp yet ignorant you might have balked at the idea of it being a plasma given near-IR photons should not be able to ionize matter to a decent degree. The reality though is these interactions are not baby's first "single-photon" tree-level diagram quantum interactions, instead the intensity is high enough you model the ionization interaction as a so-called "many photon ionization" process, where you either say many photons pile on-top of each other (which has issues in accuracy honestly) or better, the external field is strong enough it's on scale with the coulombic field at the bound electron's radius that it distorts the field seen by the electron leading to ionization[0], similar to the Stark effect but with an AC field instead of a DC field.

EDIT:re-reading the "hotter than the sun" comment, it looks like I misread it and apologize, it's not as bad as I read it. Basically, think about the natural timescale of this system and realize that the timescale needed to produce gamma rays is pretty short.

Ok, I won't bore you with figuring it out yourself, basically the whole intense interaction before material recombines is at longest a few hundred picoseconds, in fact, the electron acceleration that is MeV+ that then you can convert into x-rays happens on the optical wavelength timescale (that, yes 3fs is the natural timescale! at least for the electrons). So, you can in fact achieve KeV+ plasma "temperatures" for very short periods by focusing the energy of a plasma, ~joule or so, into small spaces (again, natural space scale is laser wavelength, although it's really the laser spot here, so say 100 wavelengths so about 10s of microns) in a short time (picoseconds) you easily achieve yes astrophysical scale temperatures for very short times and small scales--but enough to produce high energy particles and even model astrophysical phenomena! In fact it's a grant writing/masturbatory phrase we use but these systems have even been used to do so-called "laboratory astrophysics[1]" that is model astrophysical phenomena in the lab by creating plasma conditions that you can actually probe experimentally. Again, since we're all laser physicists, the fact the plasmas last picoseconds or nanoseconds isn't a problem because we use the same optical systems that create the matter to probe them that can probe the system on the picosecond scale.

One last note, this is the entire premise of inertial conefinement fusion, you create stellar core pressures and temperatures in a ~mm hohlraum for a very short time, nanoseconds, but that is enough to generate fusion conditions for the deuterium which is what matters. Ditto for creating plasma conditions for radiation generation although that's even shorter, again femto to picoseconds.

[0] https://en.wikipedia.org/wiki/Tunnel_ionization

might as well throw it in here but the usual way it is modeled is by old Russian work of ADK

http://jetp.ras.ru/cgi-bin/dn/e_064_06_1191.pdf

which is a somewhat flawed approximation of PPT

http://jetp.ras.ru/cgi-bin/dn/e_023_05_0924.pdf

[1] https://iopscience.iop.org/article/10.1088/1741-4326/aae598