The pH is high because the addition of chlorine gas is very acidic. The CYA is high because they are probably only adding chlorine once a week so to prevent chlorine loss during the day from sunlight the higher CYA is used.
As an example, let's start with 4 ppm FC, 100 ppm CYA, 120 ppm TA and a pH of 7.8. If I add enough chlorine gas to increase the FC by 10 ppm to get to 14 ppm, then the pH will drop to 7.4. As the chlorine then gets used up during the week and drops to 4 ppm FC, the pH would drop to 7.2 (and the TA would drop by 14 ppm to end up at 106 ppm) except there will probably be some carbon dioxide outgassing depending on the amount of aeration so the pH may stay near 7.4 or so, perhaps rising even higher.
So now they come by the next week and repeat the process and add some pH Up and/or baking soda in combination to get the pH back to 7.8 and the TA to 120 ppm. Then they add the chlorine gas. If the TA is higher or 50 ppm Borates are used, then the swing in pH is less.
Though some algae could potentially just start to grow in the day or two at the end of the week when the chlorine is low, it gets killed when the chlorine is then raised to the higher level. So the pool remains clear and algae free. The 4 to 14 ppm FC swing is still within normal chlorine limits with the FC staying below 15% of the CYA level so would not be irritating or noticeable.
The only thing to be careful of with this approach is that the application of chlorine gas into the pool needs to be done carefully. The flow rate for the chlorine gas needs to be such that it all dissolves into the pool and fairly evenly, so not all at the bottom of the pool (they usually put the hose into the deep end and have it pointed/bubbling upwards). This helps to prevent the acidity from damaging plaster which is the most common problem from pool services using chlorine gas that don't know how to apply it correctly. An example of a pool service that does this well is
Pool Chlor whom I visited when I went to the NEHA conference in Arizona last year (Que Hales of Pool Chlor also runs
JSPSI).
Chlorine gas is the cheapest form of chlorine so hopefully the pool service is passing on some of this savings to you.
Richard