gistfile1.cs

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Threading.Tasks;
using System.Xml;
using System.Xml.Linq;
using NuGet.Frameworks;
using NuGet.Packaging;

namespace ScriptCs.Dnx
{
    public class Program
    {
        public void Main(string[] args)
        {
            var file = @"C:\Users\filip\Documents\dev\dummy\packages.config";
            var folder = @"C:\Users\filip\Documents\dev\dummy\packages";

            var compatibilityProvider = new DefaultCompatibilityProvider();
            var folderReader = new PackageFolderReader(folder);
            var nupkgFiles = folderReader.GetFiles().Where(x => Path.GetExtension(x).ToLowerInvariant() == ".nupkg");

            var packagesConfig = XDocument.Parse(File.ReadAllText(file));

            var reader = new PackagesConfigReader(packagesConfig);
            var contents = reader.GetPackages();

            foreach (var nupkg in nupkgFiles)
            {
                var stream = folderReader.GetStream(nupkg);
                var packageReader = new PackageReader(stream);

                var identity = packageReader.GetIdentity();
                var packagesConfigReference = contents.FirstOrDefault(x => x.PackageIdentity.Id == identity.Id && x.PackageIdentity.Version == identity.Version);

                if (packagesConfigReference == null)
                {
                    break;
                }

                var packageContents = packageReader.GetLibItems().Where(x => compatibilityProvider.IsCompatible(x.TargetFramework, packagesConfigReference.TargetFramework)).
                    SelectMany(x => x.Items.Where(i => Path.GetExtension(i).ToLowerInvariant() == ".dll"));

                foreach (var packageContent in packageContents)
                {
                    Console.WriteLine();
                    Console.WriteLine(packageContent); //this will contain PATH to DLL to be loaded
                    Console.WriteLine("-----");
                }
            }

            Console.ReadLine();
        }
    }
}

Try:
var packageContents = NuGetFrameworkUtility.GetNearest(packageReader.GetReferenceItems(), packagesConfigReference.TargetFramework, g => g.TargetFramework)

packageReader.GetReferenceItems() handles the *.dll filtering for you, GetLibItems is the full list of files.

NuGetFrameworkExtensions.GetNearest is another alternative/wrapper for NuGetFrameworkUtility.GetNearest that you could use.

Your check for compatible items is close, but TryGetCompatibleItems from V2 was actually finding the nearest compatible group and returning just those items, instead of all compatible items like the name implies.