Does multi-cooker actually bake?

It doesn't necessarily do any of those things well, but yes, it does (more or less) all of the things it suggests.

Basically all cooking is the application of heat, in different ways, to food. So a multicooker like you mention is something that's capable of producing heat at different levels and different timings.

Baking differs from frying/sauteing/etc. in that some of the heat is not applied through conduction. Some of it is - the pan typically gets hot and directly heats the food where it is in contact - but some of it is either radiation or convection cooking. This probably won't do much for convection, but because it's an enclosed container, it will heat the non-contact parts through radiation if it's constructed properly (i.e., it is properly insulated, and has metal walls that will radiate heat back towards the food rather than plastic that will absorb the heat).

You'll notice it doesn't claim to roast foods (as opposed to some other multicookers); some do, and those have a heating element in the top. A pressure-cooker style multicooker can't have this (easily, anyway) and so doesn't claim any application that requires direct heat - only conduction or radiation.

Frying is cooking in oil (the oil version of boiling). Anything that can produce heat in a pan can fry (and to be good at frying, it just has to be good at maintaining a specific temperature).

Most of the features it claims are related to an ability to precisely control temperature. Yogurt making and sous-vide cooking require specific temperature control, but beyond that most of the features are just things you could do in any pressure cooker or slow cooker managed in the proper way.

The one feature it claims that I'm most dubious about is 'microwave'; it seems unlikely to me that it uses microwaves (it's too small really, for one), so probably it's claiming it can replace your microwave because it can reheat your food (the main reason many people use microwaves). There are microwave/oven combos (If you're in the US, your local Subway restaurant uses one, for example, probably made by Amana), but they're much bigger.

Either way, I don't think this is something that can 'replace' an oven or similar, because an oven is going to be much better at even heating over a period of time, and an oven is much larger (you're not roasting a turkey in here). It probably doesn't get very hot, either, compared to a good oven. The main point of multicookers is that they can do several things in the same device - so for example you can sautee your veggies and then cook a soup directly in them without involving anything else; and they do several things that you might need different devices for (saving kitchen space). They don't do them as well, but if you're in a tiny 40 sq meter apartment, perhaps that's fine.

I am able to bake cookies, bars and even bread in the Ilo multicooker.