Your first video shows the smaller (power) piston, and it's this one you may want to try sealing.
So, with a LTD (low temperature differential) engine, you don't have a lot of pressure difference to work with to drive the power piston. The seal you can achieve with a loose slip-fit on the
(brass?) piston sliding in an (aluminum?) bore is not going to be great (and thermal expansion of the different materials plays hob with the sealing as well. Test this - if you plug the port with your thumb and let the piston drop under gravity, it should take several seconds (10 or more) for the piston to drop out of the cylinder. Even that is just not good enough to get sufficient work out of the gas to keep the engine ticking over. The engine probably will work better if you put it over an open flame, and get the hot side temperature up over about 300 or 350 F. Designs I have seen that work on a cup of hot water use something like a piece of rubber balloon to seal it off; you could play with that idea on your engine and see if it helps.
But you also have a lot of potential heat leakage (conduction loss) from your engine along the displacement cylinder wall, you might try making the 4 posts holding the hot and cold plates much thinner, or hollow with thin walls, or from a very non-heat-conductive material (titanium? Hah. Plastics would likely work).
Check these two guys out - low temp. diff engines. Jan Ridder's engines (I've built several of his designs, but not the LTD Stirling...yet

work extremely well if you follow his drawings carefully, or at least follow his engineering intent, which he does a good job of explaining. His LTD engine uses a graphite piston in a glass cylinder, which can be machined and polished to achieve a very good seal, and both materials have near-zero thermal expansion, so the seal stays the same from room temperature to operating temp. And that engine can work from the heat of your hand in a cool room...pretty nifty. Myfordboy also has plans for a LTD coffee-cup engine that works well, he uses a balloon seal I think. Lots of other info out there, see sites like the ones ive posted and follow their links.
Jan Ridders site -
Myfordboy YouTube site -
also sites like this have members that love to help people build model engines (like 1/8 scale Ford 302 V8's and such) -