Why is ping faster through VPN than without a VPN?
Although it is an uncommon situation, it is possible. There could be a lot of answers.
It is probably about the internal structure of your network provider. What could help a lot, if you would give us a result of your tracert -d 1.2.3.4 command, where 1.2.3.4 is the IP what you pinged, and you would edit into your question.
Without that, I think the most probable reason is the network organization of your ISP.
The ISPs also need to pay for the network of different providers. In most cases, they are continously trying to find the cheapest / best providers, thus in most cases they use different routing for a near-area and for the far, remote locations. Of course, network for them is mostly much cheaply, while the network for the local area is mostly done by a regional organization established by a group of local ISPs or by the local government.
It is normal for the ISPs to pay only a much narrower network bandwidth from the costlier part, especially if you are from a small ISP or use a cheap package.
If you use the VPN, this VPN connected probably on the faster external network of your ISP, thus it were faster. And, the VPN provider uses probably a much faster network as your network provider.
After extension: checking the traceroutes, we can get very precise infos, what and where is the slow point in the system. Especially if we compare all of the 3 routes.
Check, were are growing the packet response time at most. In your case (the VPN-less case and in the case of the Finland VPN) it is between 83.97.88.69 and 62.40.112.215.
Checking them in an IP Whoise lookup service (for example: https://www.whatismyip.com/ip-whois-lookup/ ), we can see, that it is where your Australian packets are arriving England. It is probably a multiple sub-ocean communication cables, which is surely very costly for your cable network provider, so it tries to spare that.
What makes the things a little bit more funny: in case of your German VPN connection, that Australia -> England cable doesn't do anything. Probable the data connections into Germany are going on a highly different way.
From the Australian network configuration, there shouldn't be any difference.
I think, the reason is in your case, in Europe. The German VPN Prodiver paid a lot more to get a better global network bandwidth, as the network provider of your game server. This is the probable reason, why can it avoid that delay between .au and .uk .
The Finland VPN provider couldn't do that, and the probable reason in this case, that although Finland is a highly developed country in the region, it is probably not connected with such a well-developed global network as Germany (this, the ISP of the Finland VPN Provider had to buy a narrower bandwidth, and can't avoid the british delay).
A VPN forces traffic to take different routes.
Usually, ISPs optimise for bandwidth and cost, not for latency.
From WHOIS and reverse DNS, it looks like you are in Greece and the server is in Ireland.
First, let's take a look at the non-VPN path. The 62.40.* hops seem to have screwy reverse DNS (they are within milliseconds of each other but have reverse DNS that seems to indicate four different countries), but I would guess that the hop from 83.97.88.69 to 62.40.112.215 is actually a direct link from Greece to London.
That link seems to have a high latency, accounting for the majority of the total latency in the path. I would guess that there are two possible explanations. One is that the link may be taking a geographically indirect route such as an undersea cable through the Straits of Gibraltar. Another may be that the link is congested.
With the VPN, the traceroutes only show the hops after your traffic hits the VPN server. With the German VPN, we clearly see that traffic to the VPN server must be doing over a lower latency link than the aforementioned link to London. Most likely your Greek ISP or their upstream has a link from Greece to Germany that has a much lower latency than their link to London.
With the VPN in Finland, your traffic takes 150ms to even get to the VPN provider. I would guess your traffic is probably taking a rather indirect route to get to Finland (it wouldn't surprise me if it was going via London).
Because of routing
While you would think when you (A) ping someone else (B), the connection is A-B, there are always hops between you and B. Your packets might actually do A-C-D-E-F-B, and each connection has its own speed, latency and bandwidth.
When you ping via your VPN, they might have better routing (either random or because they pay for it), so it might be they route you A-X-VPN-Y-B, with better speed/latency/bandwith than your original path.
Or it might be worse. Both can happen.