Lubię ten rytm, bo łatwo przy nim biegać.

In Polish, the verb ending already tells you who the subject is. Lubię means I like, so ja is usually unnecessary.

• Lubię = I like
• Ja lubię = I like too, but with extra emphasis, like I like it

So in a neutral sentence, Lubię ten rytm sounds natural.

It is in the accusative case, because lubić normally takes a direct object in the accusative.

• lubić kogo? co? = to like whom? what?

So:

• nominative: ten rytm
• accusative: ten rytm

These two forms happen to look the same here because rytm is a masculine inanimate noun. For many masculine inanimate nouns, nominative and accusative singular are identical.

Because rytm is:

• masculine
• singular
• inanimate

So the demonstrative this must match it:

• nominative singular masculine: ten
• accusative singular masculine inanimate: also ten

That is why you get ten rytm.