The output stage of the LT1716 can drive loads connected
to a supply more positive than the device, the same as
comparators with open collector output stages.
And indeed LT1716 has very feeble current source capability, but decent current sink:
You are using it [wrong basically] as a current source.
It's not very clear what you asked in that comment, but for an open-collector comparator (like LM339), the load goes between its output and the positive supply rail. The LT1716 can be used even with a (lower-resistance) 1K load (at 7V), but the 1K load has to go between its output and the positive rail.
The LT1716 actually has a push-pull stage but the (high-side) PNP transistor is weak (perhaps because it is a lateral one). You can use the LT1716 with a low-side load, but it has to be of fairly high resistance (greater than 100K or so for 7V supply).
While a LM339 (which has a true open-collector output) is usable in the same manner with a high-side load:
It is not usable at all with a low-side load:
EM Fields raises a fair point that the currents/voltages on the high vs. low side load resistors are in anti-phase. This is shown below (at the top of the graph) with a (5V) CMOS [push-pull] comparator that can sink and source current almost equally well. Also shown on the below it is the same circuit but with the comparator replaced with an open-collector one (LM339). The currents are also in antiphase, but that comparator has no ability to influence the output when it's (sole) output transistor is "off", so the external circuitry dictates the off point, which in this case is at midrail because it's an equal voltage divider. The LT1716 is almost like the open-collector one because of the large difference (2-3 orders of magnitude) between the currents it can source vs. sink. Hope this helps.