"1.5 g·kg body mass⁻¹" can be equivalently written "(1.5 g)/(1 kg body mass)" or read "1.5 grams per kilogram body mass".
So, a 87 kg person would be given 130.5 g of alcohol. The units work out as:
(1.5 g EtOH)/(kg body mass) * 87 (kg body mass) = 130.5 g EtOH
That is, you have (kg body mass) in the numerator and denominator, these cancel and you end up with just the g EtOH. When working with units, it's always a good check to write out the units you have and see that the units you end up with make sense for the answer you're trying to get.
Written out another way, you have the dose per weight; you want to multiply that dose per weight by the actual weight to get the dose.
Does the 12±2 translate to 10-14 drinks?
A standard drink in the US is about 14 grams, but these authors aren't in the US. A UK standard drink is 8 grams. Australia is 10 grams. However, they write in the paper:
The alcohol ingestion protocol (1.5 g·kg−1 BM; 12±2 standard drinks) began 1 h post-exercise and was consumed in 6 equal volumes of 1 part vodka (∼60 mL) to four parts orange juice
So if they are taking a standard drink to be 30 mL vodka (approximately 1 fluid oz) and giving 12 of those. 30 ml vodka is going to be just under 10 g ethanol, so by the Australian measure that all works out.
And, yeah, that's a lot of alcohol to drink, especially over just 3 hours. The paper begins "The culture in many team sports involves consumption of large amounts of alcohol after training/competition" - they're targeting the binge level of drinking observed around team sports.