I have switched to alternative software about two years ago, and dropped Adobe applications. Here is my answer for the OP:
Photoline - yes, horrible site, but don't let that distract you!
layers: ✓ [all blend modes, plus the possibility to set layer opacity from -200 up to 200 percent! Extremely useful - an improvement over Photoshop. And every layer can have as many layer masks (both bitmap and vector) as you like: again a vast improvement over Photoshop. And here is the amazing thing: in Photoline any layer can have ANY IMAGE MODE independent of the overall image mode. This means you can combine Lab, CMYK, RGB, Greyscale, and Monochrome images together in the same layer stack! No more image mode switches! And full 8/16/32 bit per channel support for Lab, RGB, CMYK and greyscale. Very liberating. Photoshop looks old in comparison.
all layer effects: ✓ [all layer effects, plus that imported Photoshop files with layer effects are translated to Photoline layer effect equivalents. Photoline actually offers MORE layer effects than PS. For example, a 3d shadow, a 3d lighting effect, and up to three color overlays. A full range of non-destructive adjustment layers compliments Photoline layers. Since layer masks behave like ordinary layers you can even apply adjustment layers to layer masks!!
patterns: ✓ [patterns come in two flavours in Photoline: bitmaps (like PS) and true procedural textures. Both can be applied in a non-destructive manner to objects and layers.
gradients: ✓ [gradients in Photoline are applied non-destructively. Even in layer masks. Gradients are controlled through visual controls directly in the view.
smart objects: ✓☓ [Photoline's version of smart objects are 'virtual layers'. These allow you to clone and instance layers, layer groups, layer masks, anything really. Unlike Photoshop these clones update in real-time, and there is no need to open these in a separate window: the originals can be changed in the document itself, and the clones automatically update. This is actually far more flexible than Photoshop's smart objects. Also, Photoline supports externally linked placed file layers that update automatically when changes are made externally.
So both Photoline and Photoshop offer similar functionality, but have a different implementation, each with its own advantages and caveats. Level design in Photoline is very nice, because you can have all the assets organized on one or more pages, and then create virtual clones of each asset and bring them together on other pages for level designs, and so on. Good snapping and alignment tools are available as well. No more silly "layer comps" to organize your work. I have worked with large levels with thousands of vector and bitmap objects, and it works really well.
history: ✓ [Photoline supports a history palette.]
PNG export: ✓ [yes. Also an option to select layers and export all the selected layers in on go as png files.]
rescaling: ✓ [Photoline has great rescaling algorithms built-in: Lanczos 3 and 8, Catmull Rom and MitchelNetravali for high quality down scaling. All scaling and rotation of layers is non-destructive if you want. The original content is NOT resampled until export]
text (and font properties)- paths: ✓ [Photoline actually offers light DTP features, which means: multiple page support in document mode, linked text frames, good type control. Text in Photoline is fully vectorial, and can be exported as vectors easily.]
shapes: ✓ [unlike Photoshop shapes in Photoline are truly vectors, and can be output as such easily. Shapes can be used for masking, and the SVG import/export is great. Even better: Photoline offers an external application connection, which allows you to hook up InkScape, and send Photoline shapes/layers directly to InkScape, edit those, save, and the Photoline layer automatically updates when you switch back. (note: the latest betas offer this functionality - the beta can only be accessed after you purchase a license). Photoline has the essential vector editing tools. And bitmap can be converted to vector layers as well. And full pdf support (meaning shapes remain vector in an exported pdf!)
selections / color selecting: ✓ [full compliment of Photoshop level selection tools. Even better: an adjustment layer to convert any colour (range) to transparency. A black background can be removed in a matter of seconds (even black that is pre-multiplied with lighting effects). The only thing missing is a dedicated refine edge command like the one in Photoshop]
rotation: ✓ [Same as rescaling. Also non-destructive by default. No need for "ctrl-T" ;-)]
Photoline is extremely affordable, and comes with a perpetual license. You can even install it on a usb drive/stick. The installation file is a mere 20~30MB(!). And I like the fact that the beta is open to anyone who asks for it. The devs have implemented about 15 of my requests in the last 20 months.
Combine Photoline with Krita (free) for excellent digital painting and drawing (better than Photoshop), and InkScape for vector drawing, and you have a very powerful trio that arguably is an improvement over Photoshop for game asset creation (my own experience: I am an independent game dev/designer). Be sure to check out the latest beta which adds some very useful workflow enhancers.