Be careful as you read: that whole listing is dubious.
The listing is actually covering three completely different products: firstly, an HDMI-to-USB-2.0 capture card (HDMI female, USB-A male). And secondly and thirdly, red USB-C– and Lightning-to-HDMI cables (USB-C/Lightning male, HDMI male, plus USB-A male for a power source), which I will call broadcast cards for the rest of this comment, for want of a better name. Leastways, I’m pretty sure they’re broadcast cards, though the text doesn’t mention anything at all about them (except possibly for one line, discussed below), and the images and single line description in the “Item” dropdown are hardly conclusive.
The listing conveniently blurs the lines about what it’s talking about.
The capture card claims to support 4K 30fps input. Not output.
In the text, it says “Video Output Resolution: Max output can be 1080p (lightning cable)/ 4K (Type C cable)”. The mentions of Lightning and USB-C imply that this line is talking about the broadcast card… even though everything else in the listing is talking about the capture card (I think). I know the saying, “never attribute to malice what can be adequately explained by incompetence”, but I can’t explain this with incompetence. I’ve got to attribute this to malice, >99% they’re flat-out lying to make the product sound better. Adding a USB-to-Lightning or USB-A–to–USB-C adapter can’t improve a product that’s limited to USB 2.0. There is certainly no 4K output on the capture card. So by this point, we know nothing about its output, save that they lied. 1080p seems the most likely reconstruction and reconciliation of the lie.
One of the images (probably talking about the capture card) says “1920x 1080@30Hz”, but frankly I don’t believe this represents reality—even if it is mostly true, it’s certainly lying by omission. USB 2.0 simply isn’t capable of channelling full-quality video at that level (1920×1080, 3×8-bit channels, 30fps), so the only way they could hit that frame rate is by compression, meaning lowering the quality of the signal markedly.
From my research, many report USB 2.0 HDMI capture cards having terrible image quality and not even hitting 30fps consistently. I have not actually purchased any myself to verify this one way or another, but I have found quite a few reports of these sorts of thing, some in reasonable technical depth, whereas I have not found a single technically-detailed review that looks favourably upon these units. So I say avoid USB 2.0 ones like the plague, because there’s simply not enough bandwidth for them to be good products. You’ll have better luck with USB 3.0 ones, and make sure that they explicitly say 1080p/60fps output. (There are 1080p/30fps USB 3.0 ones, but they seem to be commonly associated with complaints as well, so that I imagine they’ve been cutting corners severely; so even if 30fps is all you want, I suggest getting one that advertises 60fps output—that’s what I’ll be doing when I get one.)