Learn Swedish: Vi cyklar mot grinden. - We cycle towards the gate.

The preposition mot means you are moving "towards" or in the direction of the gate, focusing on your trajectory. You might turn off the path before you get there. If you used till (Vi cyklar till grinden), it would mean the gate is your clear, final destination and you intend to arrive right at it.

Is mot only used for physical trajectories like cycling towards a gate?

No, it has a few other common meanings you will see at this level. It can also mean "against" (like a sports team playing mot another) or express how you behave towards someone, like being kind to a friend (snäll mot en vän).

Why is the word for gate spelled grinden instead of just grind?

The base noun is en grind (a gate). Because it is an en-word, you add the -en suffix to the end to make it definite, giving you grinden (the gate).

In English, we would usually say "We are cycling" here. Why does Swedish just use cyklar?

Swedish does not have a separate "-ing" (continuous) tense for actions happening right now. The present tense verb cyklar translates to both "cycle" and "are cycling", and context tells you which one makes the most sense.