Is one screw at each end enough for this cabinet cleat?

I wouldn’t judge it by the screw count alone. What matters is how much solid material each screw actually bites into, where the screws sit, and whether the cleat itself is firmly attached to the wall. A short screw with little purchase is a different situation from one that goes well into a substantial cabinet side.

Before hanging it, check the screw length and placement, and make sure the wall cleat is secured to suitable framing or another appropriate support. If you can’t confirm those details, I’d reinforce the cabinet-side connection rather than assume two screws are enough.

With material that thin, I wouldn’t just add a couple of nearby screws and hope for the best. Closely spaced holes can create their own splitting problem. If the cleat is glued as well as screwed, and the existing screws have good engagement, that may be a reasonable setup for a modest load, but I’d want to verify those details first.

If you do add fasteners, place them with enough spacing and use pilot holes sized for the screws. Another option is a connection that bears on thicker cabinet parts, if the design allows it.

Quick version: I’d be cautious about loading it until you know how much screw is actually buried in the cabinet. The bottles aren’t the only consideration, since a hanging cabinet also puts force on the cleat as it sits off the wall.

Also check the wall attachment separately. A strong cabinet-to-cleat joint doesn’t help much if the wall cleat isn’t fastened securely.