DisplayPort is compatible with Thunderbolt and therefore more flexible for use in computing applications in general.
This is actually backward. Thunderbolt is mandated to be backwards compatible with DisplayPort.
HDMI was designed primarily for AV devices, and it shows.
HDMI was born from DVI which uses the same basic signaling (hence passive HDMI to DVI adapters). The consumer market added two things to the initial spec that DVI did not have: encapsulated PCM audio and HDCP copy protection.
Professional AV gear of that time continued to utilize DVI as those two features were not hard requirements for connectivity or production purposes. While the consumer side of HDMI evolved to support high clock speeds, the professional side simply adopted dual link DVI and begun to support HDCP for ease of bringing in an HDMI signal here necessary. The newest generation of professional gear are adopting DP natively where as the consumer side is still focused on HDMI.
1. DisplayPort has supported variable refresh rates (VESA adaptive sync) for years; HDMI just added support for VRR in January of this year, and I'd be surprised if many devices even support it yet.
Adaptive sync is an optional extension for DP. Similarly it is not a hard requirement either on the HDMI. DP was able to incorporate variable refresh in a pretty straight forward manner due to how DP utilized a self clocking signal. HDMI on the other hand has dedicated pins for the clock signal.
2. DisplayPort could do 2x 4K @ 60 Hz since 2014. HDMI could only do one until this year.
This is incorrect. DP 1.4 with DSC has enough bandwidth to drive two 4K displays at 60 Hz but the hardware to support that was only released in 2016. This still isn't technically possible either as there are no DP 1.4 MST hubs on the market.
HDMI 2.1 has enough bandwidth to do this in the spec but it would require utilizing Twin View which carries some complexity. Twin View essentially splits the data stream as if it were a 3D display but the signal for each eye is not bound to a single display.
The only way to get two 4K @ 60 Hz displays out of one physical connector today is via Thunderbolt 3 which encapsulates two full independent DP 1.2 streams. Even then, this is optional (Thunderbolt 3 only requires a single DP stream to be encapsulated) and thus some Thunderbolt 3 ports are limited to a single 4K display output.
3. DisplayPort supported 8K a year before HDMI did.
Two and a half years if you go by when each spec was ratified.
If you go by shipping hardware, HDMI 2.1 gear has not yet arrived on the market so 8K via HDMI is yet not possible. The first HDMI 2.1 capable hardware is not expected until late 2018 which would still be two years.
Any PC-related functionality has been incorporated into DisplayPort in a much more timely fashion. If you want to support the best displays and play at the high end of the market, you could not compete by offering only HDMI/mini-HDMI.
The real problem HDMI is running into is bandwidth over copper cabling. Active HDMI and active-fiber cables are not formally part of the HDMI spec and only conform to a specific version (ie fiber HDMI 1.4 cables cannot work at HDMI 2.0 speeds). These active cables are also directional which complicates installation.
DP on the other hand does support active cabling as part of the spec to support longer distances and higher bit rate. The core reason for DP's greater flexibility here is that it mandates a far higher auxiliary power to supplement these features.
Once it became the standard for PCs, it becomes difficult to justify the additional space for HDMI connectors, especially since DisplayPort can support HDMI-out with a passive adapter---the reverse is not true. (Note the "can"; the standard does not require that all DisplayPort outputs support it.)
Passive adapters are actually an optional part of the DP spec (formally DP++). Active adapters will always work for converting DP to HDMI though.