This rather misrepresents the study's finding, which is given in summary at the paper link as follows:
"Only increased dietary fat content was associated with elevated energy intake and adiposity. This response was associated with increased gene expression in the 5-HT receptors, and the dopamine and opioid signaling pathways in the hypothalamus. We replicated the core findings in four other mouse strains (DBA/2, BALB/c, FVB, and C3H). Mice regulate their food consumption primarily to meet an energy rather than a protein target, but this system can be over-ridden by hedonic factors linked to fat, but not sucrose, consumption." (Italics mine.)
The dietary fat caused mice, who eat to meet an energy requirement, to override their natural instincts because fat tastes so good (or, rather, it gave them an addictive high) which made them increase their energy intake unnecessarily. The fat they ate didn't make them put on weight, but the eating over and above their energy requirement did.
Once again, you can lose weight however suits you best, because (varying metabolism rates aside) if you consume more energy than you expend you will gain weight, and if you consume less energy than you expend you will lose weight -- as shown by these mice.