TL;DR - Unfortunately you can't use the ULINK2 with the Atmel AT89S8253.
ULINK2 supports the ATMEL family of 8051 controllers (reference: http://www.keil.com/dd/).
Unfortunately you have misunderstood what that webpage shows. The "Legacy Device List" (it used to be called "Device Database" until MDK5 was released) is described by Keil here where they say:
"The Device Database is a searchable database that contains information about the various microcontrollers supported by software development tools from Keil.
The online Device Database entry for each device explains which features are supported." [My emphasis]
Therefore you can see that having an entry in the old Device Database does not mean that the ULINK2 is supported by that device. It just means that some features of the Keil range of software development tools are supported by that device. You have to view the specific webpage for that device, to see which features (e.g. ULINK2) are supported.
The Device Database page for the Atmel AT89S8253 does not mention the ULINK2 at all. That lack of mentioning ULINK2 is telling you that ULINK2 is not supported with that target device (I will explain why below). Whereas the Keil CA51 compiler kit is supported on that device, since this is listed.
Compare that with, for example, the Device Database page for the NXP (Philips) P89LPC952 which specifically lists:
Here is why the ULINK2 is not compatible with the Atmel AT89S8253:
As you can see in the Atmel AT89S8253 datasheet from the Keil website, there is no mention of a JTAG (or SWD) interface on that IC. However as described here in the ULINK2 webpage discussing the initialisation sequence with 8051-type devices, the ULINK2 uses a JTAG (or SWD) interface with the target device:
However the P89LPC952 datasheet from the Keil website (which I mentioned as an example of a different 8051-style device earlier) shows that it does have a JTAG-style (really SWD) debug interface:
This explains why that device is compatible with the ULINK2 and why its listing in the Device Database does mention the ULINK2 (unlike the listing for the Atmel AT89S8253).
In summary: The Atmel AT89S8253 does not have the required JTAG/SWD debugger interface to connect to a ULINK2, and Keil do not claim that the ULINK2 is compatible with that target device. Some other 8051-type device do have a JTAG/SWD debugger interface e.g. the NXP (Philips) P89LPC952.