Derailleur replacement recommendation
According to your link - your bike is 8 speed.
The bog standard (excludes the upper-end XT variant) Deore derailleur has only ever been produced in 9/10 speed.
And one assumes - you are looking at the latest 10 speed version.
An 8 speed chain is significantly wider than a 10 speed chain. Consequently, the chain may have problems with not only the jockey wheels of a 10 speed derailleur but also passing through the cage of the mechanism.
Additionally, MTB rear mechs - can run much wider range of gears and therefore can have a longer cage to facilitate this. With the range of gears on the link - you would require a medium cage rear mech.

You bike runs the Shimano 2300 range. And I would recommend sticking to this or something like the Shimano Claris range. These are also road specific &amp; probably cheaper than a Deore rear mech.