First question, what are you trying to achieve? Do you want to replace a bad cylinder or change out the sleeve it fits into or the base to change the height of the chair or repurpose some of the pieces for something else? E.g. if it’s just the cylinder then the sleeve can stay where it is, see below about releasing the cylinder.
OK, if the sleeve has to come out, first of all take the ram cylinder out of the tube that fits into the chair base, that little circlip on the bottom releases it. A hand full of bits will come with it including a thrust bearing and spacers.
Then, find/make a jig that the tube will slip into and support the assembly inverted by the chair base. I’ve used a 5 gallon bucket but you need something more robust and that will protect the chair base. Your jig wants to be something rigid like a hunk of pipe sitting on a concrete floor so when you hit it the force isn’t absorbed by the support jig.
I typically start with a 3 lb ball pien but when I get a stubborn one I get out the 8 lb sledge. With the chair base firmly supported, a good firm blow should release the sleeve. The 8 lb is good because it leverages lb-ft vs ft/sec., you can get a good thump of energy without a big swing.
Protect the end of the sleeve with a piece of hardwood and put something below the sleeve to cushion it when it pops free……I know this, LOL!
There is a 2-1/2 degree included angle on the base/tube interface.
Good luck!
D