A wired connection would improve connection stability yes, but as celegorm implies - the actions of the other machines in the network at the time will influence your performance much
Unfortunately modern routers have more RAM in them than they used to, and I say unfortunately because more RAM in your router actually makes your connection quality decrease
. This is all due to the nature of buffering.
By definition, larger buffers 'hold on' to data for a longer time period, so if other machines are using the connection at the same time as you (or your own machine is doing more than one thing - i.e. downloading windows updates or AV signatures while playing games) then more of your game data sits in these buffers waiting for the other traffic to be processed before reaching your computer. Worse still, if this data is sent over a TCP connection and a packet has been dropped en-route it takes even longer to realise (due to the latency introduced by the buffer) and instigate a retransmission. All this results in poor quality performance for all
real-time services (the file downloading is also affecting by the gaming connection, but this isn't perceivable to the user like voice and video are). See https://en.wikipedia.org/wiki/Bufferbloat
for more information on this very fascinating and counterintuitive (at first) subject!
Assuming: your speedtest results are consistent; other users in your network are not active; and the problem persists, an alternative cause for your original problem is that your ISP is throttling game-network traffic. This is fairly easy to achieve and should also be fairly easy to determine if you search for gaming network performance for 'myISP' customers.
Good luck, hope you find a resolution for this (incidentally, there are solutions for the buffer bloat problem also - different buffer allocation and packet ordering algorithms - so if that is
your problem, don't assume you're at a dead-end.)