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I am trying to get the following RPI3B+ to work. Apparently the machine is booting ok, since I can see it using nmap on my local network:

# nmap 192.168.0.23
Starting Nmap 7.70 ( https://nmap.org ) at 2019-07-09 17:37 CEST
Nmap scan report for 192.168.0.23
Host is up (0.0056s latency).
Not shown: 996 closed ports
PORT STATE SERVICE
111/tcp open rpcbind
139/tcp open netbios-ssn
445/tcp open microsoft-ds
8080/tcp open http-proxy
MAC Address: B8:27:EB:1F:09:2E (Raspberry Pi Foundation)

But I get no display, if I zoom right next to HDMI connector here is what I see:

One of those four components seems to be sideways. Would that explain why I get nothing on the screen ? Is that even fixable ?

While I can't specifically identify them from this picture where any markings they may have are hidden, that is almost certainly the problem with your HDMI output. If you look at the three that are not sideways, you can see that solder goes from their connectors down to the runs on the board. It appears each one has four connections, and the two presumably necessary connections visible in your picture are clearly broken. This appears to be from damage after manufacture, as there is also solder coming up off of the pads that appears to have separated from the component. As the pads were not lifted from the circuit board, what is visible could be probably fixed with the appropriate equipment, but there is no guarantee that other physical damage isn't present.

While the official Raspberry schematics don't tell a thing about these components we can learn from the picture of the PCB that they are connected to the paired pins 1 and 3, 4 and 6, 7 and 9, 10 and 12 - that's all the differential signal and clock lines.

Since the devices have just four pads (not six) they are not dual-rail clamp ESD protectors, e.g. see here, as these would need to be connected to GND and VCC too.

As they are connected to the paired lines of the differential signals these devices are very likely Common Mode Filters to suppress EMI, e.g. see here.

This is how it they are connected in the differential circuit (source). Note that if they are missing or not properly connected the circuit is broken - thus no display is working:

And this is how they look - pretty much like the stuff mounted to the Pi - (source):

Suggested repair: try to resolder the component if you have the equipment and skills to do so. Make sure to not thermally damage the component. Note that high speed TMDS differential signal routing at high frequencies is rather critical. Parasitic loads and asymmetries to the transmission lines may disturb the signals to the point of a failing transmission.