What are some good ways a father can engage a toddler boy who is 1 year and 8 months old?

At 20 months, my oldest was like yours - very physical. So, the main thing I did with him was to take him outside to play. Running around, climbing on the playground, climbing stairs; all of this within reasonable safety limits, though often a bit outside what others were comfortable with, but I knew my son's limits and how careful he was. Obviously this has some limits during COVID, but hopefully you have some safe options. Expect to do this every day, or close to it, for a few hours when possible; we probably went out 5x/week or more for an hour or two at a time when he was that age, in addition to outside time he got in daycare.

Inside the house - make sure he has lots of space to run. We have a circular path around our kitchen/dining area that the kids can run, and they do that very often. You'd think they'd tire of a loop about 20 meters in circumference, but - no.

You can also get some climbing-related toys for inside the house; it's possible to have a bar in a doorway at a safe, appropriate height, only put in place when you're there to watch him, or various other kinds of 'indoor gyms'.

Finally, watch to see what he's interested in. He will get interested in other things than running around; expose him to as much as you can, and see what sticks. Just have patience, and don't assume you can guess what he's interested in.

And just to be clear - I think these recommendations apply equally for boys and girls. Some kids just like to be active, no matter their sex.