Videogame.pro is an excellent fit with the .pro extension, I think you'd sell it easily with the right .pro conditions and for more than your $250 BIN. Videogame.tv has received 6 bids on Sedo and Videogame.mobi has received 1 so it's a desirable keyword combined with extension goodness of fit.
The main reason it's not selling is it's usually used as a 2 word expression and .pro hasn't reached the point where 2 word phrases are desirable on the aftermarket. Very few domainers reg .pros and even fewer buy .pros on the aftermarket so you are probably advertising this to about 20 potential buyers on Namepros.
Another downside with the keyword is that it was more commonly used in the 70s and 80s than it is now. It's a bit like "personal computer" or "micro computer" but not as outdated. Nowadays people talk about games rather than video games. If you mean something other than a "video game" game you would add an extra word on like "board" or "card".
Offset against that, game playing online is on a steep upslope so the value of any keyword, even a formal and slightly old fashioned one like "video game", will go up so I think it would be a good investment for anybody buying it.
The problem with selling mid-teir .pros, is when you can still register short commercial single words like Pest.pro for $75, it's a tricky pricing proposition.
I regged Display.pro (3.06, 2,593.8, 20.1/15.7, 86.7m), Leads.pro (10.57, 1,242.1, 28.6/21, 23.8m), Desk.pro (3.41, 9,968.3, 7.8/22.1, 15.4m) Battery.pro (2.47, 8,808.90, 10.4/17, 15.3m), Gear.pro (1.81, 7,771.8, 9.7/4, 24.7m), Total.pro (1.51, 2,167.20, 12.1/14.1, 169m) and Manual.pro (0.92, 6,262.4, 21.1/24.1, 27.4m) today.
I've added the brackets to explain how I analyse .pros. The brackets are ($PPC estimate, daily clicks benchmark, "Pro" and "Professional" goodness of fit %'s, total Google uniques). My total Google uniques are coming up lower than usual so the last number is only a relative comparison.
The goodness of fit %'s are the Google uniques of the keyword and pro or professional in a Google search box devided by the total Google uniques of the keyword. It gives me an idea of how frequently the keyword appears with either "pro" or "professional" on the same web page.
On this basis Videogame.pro would score (1.42, 768.10, 23.3/14.7, 6.8m) so the 7 .pros I regged today outperform it on 3 of the 4 domain value parameters each time. I don't mean to criticise Videogame.pro, I'm just pointing out how someone who buys .pros on the aftermarket might analyse .pro value.
If you compare what I regged today and Videogame.pro to something I bought on the aftermarket like Mobile.pro $2,000 (2.65, 21,010.50, 37.4/31.3, 80.4m) or Training.pro $1,800 (3.24, 13,511.50, 30.7/77.4, 43.3m) it's a whole different ball game in terms of the benchmark scores a buyer would be looking for.