Not sure I understand your question. Are you asking whether the computer speed determines how well a "1300 computer player" plays?
It depends on the software, but in general I'd imagine that computer speed only determines how long the software takes to move. So if you have a fast computer, then 1300 will move quickly; if a slow computer, slowly. But in either case I would expect it to play at the same strength.
Ofcourse the speed of your computer determines whether an engine actually plays at it's designated level, but for computers to play at a below 2000 level is so easy nowadays that speed won't make any difference. I think the speed of your computer will start to matter when you get halfway in the 2000's
Many chess softwares detect hardware and declare their rating acordingly so don't bother about that. Fritz 2 played at 2150 ( which is good enough to beat all players other than masters ) and now they have come up with fritz 12 !! These monsters are too strong even on relatively slower machines. The rating you get against them is fairly accurate.
When you go higher in rating of the computer opponent, how reliable is that? I'm not talking about human vs computer, but the speed of calculation and speed of your computer. That at some point your own computer might be not fast enough to allow your chess engine to be "rated" as good as it is announced. The highest opponent I have played was 1300 ELO rating, so I'm nowhere near at the moment but this is bugging me for the future. Hope you understood my question. I know there might not be a good anwer but only speculation but all is good.