The lasers used in the McDonald Observatory experiments from 1969 onwards may not have quite exceeded the one gigawatt threshold initially, but they were certainly close, even back then.
With pulsed-laser ranging, it’s crucial to send out as many photons as possible (to increase one’s chances of detecting the “return” signal) in as short a time as possible (since fine distance measurement relies on short laser pulsewidths). A high repetition rate is also a bonus, in order to get good signal-averaging.
According to the above-linked pdf (5th page), the ruby laser’s Q-switch dumped the first (i.e. oscillator) stage in around 4ns. This was typically amplified in the three following stages up to 3 Joules per pulse.
Let’s say that the resulting output maintained the 4ns pulsewidth (they don’t show the temporal pulse shape in the paper, but the following page says: “The statistical fluctuation in the range measurement for a single pulse is roughly ± 2 nsec because of the laser pulse length and some jitter in the photomultiplier”, which supports a ~4ns output pulsewidth).
Then, 3 Joules of laser energy in 4ns gives a peak power – which is what counts in this type of experiment – for the 1969-era laser of 0.75gigawatts.
Now, the average power of that ruby laser would only have been around 1W (a 3 Joule pulse every 3 seconds), but it’s the peak power that made the experiment feasible. It just took them a long time to accumulate good data with the laser only firing once every 3 seconds…
By comparison, if one considers the laser in the Mythbusters clip (the Apache Point Observatory Lunar Laser-ranging Operation, or APOLLO): the setup starting a few years ago is described in this PDF (page 4, bottom). The energy per pulse is 115mJ (cf. 3J in 1969), but the pulsewidth is now 120ps (cf. 4ns in 1969), which gives just under 1 gigawatt peak power – not that much more than the 1969 experiment! The laser’s pulse repetition rate at APOLLO is now 20Hz (cf. 0.33Hz in 1969), so it takes a lot less time to get good data.
*[And the guy in the video comparing the 1mW of a laser pointer with the 1GW of the pulsed APOLLO laser? Average vs peak, apples vs oranges. The average power of the APOLLO laser is around 2.3W, which doesn’t sound nearly as impressive… since the laser pointer is a continuous-wave device as opposed to pulsed, its peak and average have the same value.]