James Watt made important contributions as an inventor and engineer, including an improved steam engine and other inventions, but his closest field of science was chemistry, and that's not what he's most known for anyways.
Out of all the SI units, base and derived, I think the watt is the only one named for someone not a prominent physicist.
Well, he was the one who devised, defined, the unit of a horsepower, the first quantification of power. I don't know who first specified a watt: it was a British Association for the Advancement of Science conference in 1882 that did it, so some patriotic prejudice was likely involved, as well as the fact that a steam engine was the pre-eminent source of power then. But it still makes sense to name a unit of power after him. The horsepower ( 33,000 pounds lifted one foot in one minute, 550 lbs lifted one foot in one second, etc.) is actually an optimistic notion of what work an average horse can do in a day, but Watt was apparently looking at large Scottish draft horses, not the average horse.
The designer of the first truly practical steam engine, he'd been able to re-work the earlier Newcommen design because he could accurately assess heat, and of course a steam engine is a heat engine. Watt and his business partner Boulton collected fees- royalties- from mine owners based on how much coal the mine owner saved by using a Boulton and Watt engine, as opposed to an earlier Newcommen engine. Watt was highly inquisitive anyway, and likely would have figured it out regardless, but since the company was being paid based on how much work its engines were doing, Watt was highly motivated to quantify work. He not only created and defined a horsepower, he also invented the first steam indicator, a device that shows the work being done in the steam cylinder as the piston moves, a very important gauge of efficiency in steam engines. He may not have been what we'd call a physicist, but for the 18th c. he came close enough.
Watt was not the only one. Faraday for example was not studied in the classical sense and he has a unit named after him. The Farad.
Maybe you have a black & white idea of what a physicist looks like or should be. Is a physicist someone that only practices theoretical physics? Watt's contribution to the major physics field of thermodynamics was important. So what if he happened to make practical use of his discoveries and a bit of money. He's a physicist in my book.